CBSE Class 9 Maths Coordinate Geometry Assignment Set 02

Question 1. In which quadrant, the point P(x, y) will lie?, where x is a positive and y is a negative number.
Answer: Fourth Quadrant
In simple words: When the x-coordinate is positive and y-coordinate is negative, the point is located in the fourth quadrant.

Exam Tip: Remember the signs for all four quadrants: I (\(+, +\)), II (\(-, +\)), III (\(-, -\)), and IV (\(+, -\)).

Question 2. Write the name of the point of intersection of coordinate axes.
Answer: Origin
In simple words: The fixed point where the horizontal axis (x-axis) and vertical axis (y-axis) cross each other is called the origin.

Exam Tip: The coordinates of the origin are always written as \((0, 0)\).

Question 3. Define quadrant.
Answer: The two coordinate axes divide the Cartesian plane into four parts, and each part is called a quadrant.
In simple words: A quadrant is one of the four quarters into which the coordinate plane is divided by the x-axis and y-axis.

Exam Tip: Quadrants are numbered anti-clockwise starting from the top-right as I, II, III, and IV.

Question 4. Write the x-coordinate of a point which lies on y-axis.
Answer: 0
In simple words: Any point lying directly on the vertical y-axis has a horizontal distance (x-coordinate) of zero.

Exam Tip: The general form of any point on the y-axis is \((0, y)\).

Question 5. What is the sign of the x-coordinate of a point in third quadrant.
Answer: Negative (\(-\))
In simple words: In the third quadrant, both x and y coordinates are negative.

Exam Tip: Always look at the horizontal direction first: moving left from the origin gives a negative x-value.

Question 6. If a point P(2,3) lies in first quadrant then what will be the coordinate of point Q opposite to it in fourth quadrant having equal distant from both the axes ?
Answer: \((2, -3)\)
In simple words: Equal distance from both axes means the numerical values of coordinates remain the same, but the point in the fourth quadrant has a negative y-coordinate.

Exam Tip: The distance from the y-axis is given by the x-coordinate (2 units), and distance from the x-axis is given by the y-coordinate (3 units).

Question 7. In the fig. given below, name the point whose abscissa and ordinate both are positive and write the abscissa and ordinate of the point E :
Answer: Point whose abscissa and ordinate both are positive is D (\((5, 2)\) or similar from standard graph). For point E, abscissa = \(-5\), ordinate = \(-5\).
In simple words: The point in the first quadrant has both positive coordinates, while point E has negative values for both directions.

Exam Tip: Abscissa refers to the x-coordinate and ordinate refers to the y-coordinate.

Question 8. Write the answer of each of the following questions:
(i) What is the name of horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane?
(ii) Write the coordinates of the point where these two lines (as described above) intersect.
Answer:
(i) The horizontal line is called the x-axis and the vertical line is called the y-axis.
(ii) The coordinates of the point of intersection are \((0, 0)\) (the origin).
In simple words: The coordinate system uses an x-axis and a y-axis which intersect at the origin point \((0, 0)\).

Exam Tip: Memorize standard definitions as they are frequently asked in 1-mark and 2-mark questions.

Question 9. A point is at a distance of 4 units from x axis and 5 units from the y axis. Represent the position of the point in the Cartesian plane and also write its Cartesian coordinates.
Answer: The Cartesian coordinates can be \((5, 4)\), \((-5, 4)\), \((5, -4)\), or \((-5, -4)\) depending on the quadrant. Assuming the first quadrant by default, the coordinates are \((5, 4)\).
In simple words: The distance from the y-axis gives the x-coordinate (5), and the distance from the x-axis gives the y-coordinate (4).

Exam Tip: Distance from y-axis = x-coordinate (abscissa); distance from x-axis = y-coordinate (ordinate).

Question 10. Find the value of x and y if:
1) (x-3, 7) = (5,7)
2) (2,2y-3)=(2,7)
Answer:
1) Equating the corresponding x-coordinates:
\(x - 3 = 5\)
\(x = 5 + 3 = 8\)
2) Equating the corresponding y-coordinates:
\(2y - 3 = 7\)
\(2y = 7 + 3 = 10\)
\(y = \frac{10}{2} = 5\)
In simple words: Two ordered pairs are equal if and only if their corresponding first elements are equal and their corresponding second elements are equal.

Exam Tip: Always equate corresponding components component-by-component for coordinate equality.

Question 11. From the graph below determine the coordinates of the points A, B, C and D.
Answer:
Point A = \((0, 3)\)
Point B = \((-2, 0)\)
Point C = \((-3, -4)\)
Point D = \((0, -7)\)
In simple words: Read the horizontal position (x) first, followed by the vertical position (y) for each marked point on the grid.

Exam Tip: Points lying on axes will have one coordinate as zero.

Question 12. Plot the coordinates A (-4, 0) and B (3, 0) on the coordinate plane hence finds:
1) Distance of A from origin.
2) Distance of B from origin.
3) Distance between points.
Answer:
1) Distance of A\((-4, 0)\) from origin = \(|-4| = 4\) units.
2) Distance of B\((3, 0)\) from origin = \(|3| = 3\) units.
3) Distance between points A and B = \(3 - (-4) = 3 + 4 = 7\) units.
In simple words: Distance is always positive. Add the individual distances from the origin when points lie on opposite sides of the y-axis.

Exam Tip: For points on the same axis, the distance between them is the absolute difference of their coordinates.

Question 13. In which quadrant does the following points lies?
1) A(-1, 2)
2) B(2, 2)
3) C(3,-2)
4) D(-2,-2)
Answer:
1) A\((-1, 2)\) lies in Second Quadrant (\(-, +\)).
2) B\((2, 2)\) lies in First Quadrant (\(+, +\)).
3) C\((3, -2)\) lies in Fourth Quadrant (\(+, -\)).
4) D\((-2, -2)\) lies in Third Quadrant (\(-\, -\)).
In simple words: Check the positive or negative sign of each coordinate to determine its quadrant location.

Exam Tip: Ordered pairs are position-dependent; \((x, y) \neq (y, x)\) unless \(x = y\).

Question 15. If we plot the coordinate points A(-1, 0) , B(0, 1) , C(0,-1) and D(-1, 0) on Cartesian plane . Which figure comes out after joining the Points? Also find the side of figure.
Note: Assuming the points form a geometric shape based on standard coordinates (with A and D overlapping or forming a polygon). Let points be A\((-1, 0)\), B\((0, 1)\), C\((1, 0)\), D\((0, -1)\) or similar standard rhombus vertices.
Answer: Joining points A\((-1, 0)\), B\((0, 1)\), C\((0, -1)\) and D\((-1, 0)\) forms a line segment or degenerate triangle. If points are A\((-1,0)\), B\((0,1)\), C\((1,0)\), D\((0,-1)\), it forms a rhombus.
In simple words: Plot each point carefully on graph paper and connect them in order to identify the resulting geometrical shape.

Exam Tip: Use distance formula \(\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\) to find side lengths when necessary.

Question 16. What is the distance of a point (7, -6) from x-axis and y-axis?
Answer:
Distance from x-axis = \(|-6| = 6\) units.
Distance from y-axis = \(|7| = 7\) units.
In simple words: The distance from the x-axis is given by the absolute value of the y-coordinate, and the distance from the y-axis is given by the absolute value of the x-coordinate.

Exam Tip: Distances are always expressed as positive real numbers.

Question 17. Which of the following points: B(1, 0), C(0,1 ), E (-1, 0), F ( 0, -1), G (4, 0), H (0, -7)
(i) lie on x -axis?
(ii) lie on y - axis?
Answer:
(i) Points lying on x-axis (where y = 0): B\((1, 0)\), E\((-1, 0)\), G\((4, 0)\)
(ii) Points lying on y-axis (where x = 0): C\((0, 1)\), F\((0, -1)\), H\((0, -7)\)
In simple words: Points with a y-coordinate of zero lie on the x-axis, and points with an x-coordinate of zero lie on the y-axis.

Exam Tip: Quick check: \((x, 0)\) is on x-axis; \((0, y)\) is on y-axis.

Question 18. Locate the points (3, 0), (-2, 3), (2, -3), (-5, 4) and (-2, -4) in Cartesian plane. Also find the quadrant.
Answer:
- \((3, 0)\): Lies on the positive x-axis (No quadrant)
- \((-2, 3)\): Second Quadrant
- \((2, -3)\): Fourth Quadrant
- \((-5, 4)\): Second Quadrant
- \((-2, -4)\): Third Quadrant
In simple words: Plot each coordinate by moving horizontally along the x-axis first and then vertically along the y-axis.

Exam Tip: Points lying directly on axes do not belong to any quadrant.

Question 19. Find the value of x and y if: \((2x - \frac{3}{2}, 4y - \frac{7}{2}) = (\frac{5}{2}, \frac{3}{2})\)
Answer:
Equating x-coordinates:
\(2x - \frac{3}{2} = \frac{5}{2}\)
\(2x = \frac{5}{2} + \frac{3}{2} = \frac{8}{2} = 4\)
\(x = \frac{4}{2} = 2\)
Equating y-coordinates:
\(4y - \frac{7}{2} = \frac{3}{2}\)
\(4y = \frac{3}{2} + \frac{7}{2} = \frac{10}{2} = 5\)
\(y = \frac{5}{4}\)
In simple words: Equate the first parts on both sides to solve for x, and equate the second parts to solve for y.

Exam Tip: Take common denominators carefully when adding fractions.

Question 20. See figure, and write the following:
1) The points identified by the coordinates (1, 2) and (- 1, -2)
2) The coordinate of A, B, C and D.
3) Abscissa of point C.
Answer:
1) Point for \((1, 2)\) and point for \((-1, -2)\) can be identified from the given graph.
2) Coordinates of A, B, C, D depend on the specific grid markings (e.g., A = \((0, 4)\), etc.).
3) Abscissa of point C is the x-coordinate of point C.
In simple words: Read coordinates directly from the axes corresponding to each labeled point.

Exam Tip: Always write x-coordinate first followed by y-coordinate inside parentheses.

Question 21. Plot the points (x, y) given in the following table on the plane, choosing suitable units of distance on the axes:
X: -1, 2, 0, 3, 2
y: 3, -5, -3, -3, 1
Answer: The coordinate pairs to plot are: \((-1, 3)\), \((2, -5)\), \((0, -3)\), \((3, -3)\), and \((2, 1)\).
In simple words: Combine each value of x with its corresponding value of y to form five distinct coordinate points and plot them on graph paper.

Exam Tip: Ensure axis scales are uniform and clearly labeled.

Question 22. What will be the position of point A(2, 1) if:
1) Abscissa is multiplied by -1?
2) Ordinate is multiplied by -2?
3) Point each coordinate is multiplied by -3?
Answer:
1) New point = \((-2, 1)\)
2) New point = \((2, -2)\)
3) New point = \((-6, -3)\)
In simple words: Multiply only the x-coordinate for part 1, only the y-coordinate for part 2, and both coordinates for part 3.

Exam Tip: Abscissa = x-coordinate, Ordinate = y-coordinate.

Question 23. Plot the following points in a Cartesian plane: (-2,4), (3,-1), (-1, 0), (1, 2) & (-3, -5)
Answer: Points to plot: \(-2,4\) in quadrant II; \(3,-1\) in quadrant IV; \(-1,0\) on negative x-axis; \(1,2\) in quadrant I; \(-3,-5\) in quadrant III.
In simple words: Locate each pair of numbers by moving along x and y axes respectively and mark the points clearly.

Exam Tip: Label each plotted point with its respective coordinates.

Question 24. Observe the fig. given below and answer the following:
(i) The coordinates of B.
(ii) The Coordinates of C.
(iii) The point identified by the coordinate (-3, -5).
(iv) The abscissa of the point D.
(v) The coordinates of H.
Answer:
(i) Coordinates of B = \((-5, 2)\)
(ii) Coordinates of C = \((5, -5)\)
(iii) Point identified by \((-3, -5)\) = Point E (or as per grid)
(iv) Abscissa of point D = 4
(v) Coordinates of H = \((-5, -3)\)
In simple words: Trace perpendicular lines from each point to the x and y axes to find their respective coordinates.

Exam Tip: Abscissa is the x-value; ordinate is the y-value.

Question 25. Determine the quadrants in which the following points lie;
(i) A (1,1)
(ii) B (2,4)
(iii) C (-3, -10)
(iv) D (-1,2)
(v) E (1,-1)
(vi) F (-2,-4)
(vii) G (-3, 10)
(viii) H (1,-2)
Answer:
(i) A\((1, 1)\): First Quadrant
(ii) B\((2, 4)\): First Quadrant
(iii) C\((-3, -10)\): Third Quadrant
(iv) D\((-1, 2)\): Second Quadrant
(v) E\((1, -1)\): Fourth Quadrant
(vi) F\((-2, -4)\): Third Quadrant
(vii) G\((-3, 10)\): Second Quadrant
(viii) H\((1, -2)\): Fourth Quadrant
In simple words: Determine quadrants based on coordinate signs: I\((+,+)\), II\((-,+)\), III\((-,-)\), IV\((+,-)\).

Exam Tip: Memorize the four quadrant sign rules to answer instantly.

Question 26. A car starts from the center of city and in each consecutive hour it covers a distance of 15km (along north), 5 km (along east), 15 km (along south) and 10 km (along west) respectively. Assuming the centre of city to be the origin, north-south direction is along y axis and west-east direction is along x axis; show the various position of the car on the Cartesian plane. Also, find how far is the car from x and y axis respectively at its final position.
Answer:
Starting point = \((0, 0)\)
After 1st hour (15 km north): \((0, 15)\)
After 2nd hour (5 km east): \((5, 15)\)
After 3rd hour (15 km south): \((5, 0)\)
After 4th hour (10 km west): \((-5, 0)\)
Final position = \(-5, 0\).
Distance from x-axis = 0 units.
Distance from y-axis = \(|-5| = 5\) km.
In simple words: Track movements step by step by adding/subtracting along x (east/west) and y (north/south) axes.

Exam Tip: North and East are positive directions; South and West are negative directions.

Question 27. See the figure, and write the following:
1) The coordinates of B.
2) The point identified by the point (-3, -5).
3) The abscissa of point D.
4) The ordinate of the point E.
5) The point identified by the coordinates (2, -4).
Answer:
1) Coordinates of B = \((-5, 2)\)
2) Point identified by \((-3, -5)\) = E
3) Abscissa of point D = 4
4) Ordinate of point E = \(-5$
5) Point identified by \((2, -4)\) = C
In simple words: Read graph coordinates carefully by locating the horizontal and vertical positions for each queried point.

Exam Tip: Double check x (abscissa) and y (ordinate) values before writing final answers.

Question 1. What is the name to the horizontal and vertical line in a coordinate system?
Answer: The horizontal line is the x-axis and the vertical line is the y-axis.
In simple words: The two reference lines in a Cartesian coordinate system are called the x-axis and y-axis.

Exam Tip: These two axes intersect at right angles at the origin.

Question 2. The origin is indicated by what coordinates?
Answer: \((0, 0)\)
In simple words: The origin has zero horizontal distance and zero vertical distance.

Question3. How many Quadrants are there in the Cartesian Plane?
Answer: 4
In simple words: The coordinate axes divide the plane into four equal regions called quadrants.

Exam Tip: Numbered I, II, III, IV in counter-clockwise order.

Question 4. In which Quadrant will the coordinates (-2,3 ) lie?
Answer: Second Quadrant
In simple words: A negative x-coordinate and positive y-coordinate place the point in quadrant II.

Exam Tip: Sign convention for Q2 is \((-,+)\).

Question 5. in which Quadrant will the coordinates (-3, -4) lie?
Answer: Third Quadrant
In simple words: Both negative coordinates indicate the third quadrant.

Exam Tip: Sign convention for Q3 is \((-,-)\).

Question 6. What is the abscissa and the ordinate in the coordinates (3, -5)
Answer: Abscissa = 3, Ordinate = \(-5$
In simple words: Abscissa is the x-value (3) and ordinate is the y-value (\(-5\)).

Answer:
- For \((0, 3)\): Abscissa = 0, Ordinate = 3
- For \((3, 0)\): Abscissa = 3, Ordinate = 0
- For \((0, 0)\): Abscissa = 0, Ordinate = 0
In simple words: First number in each pair is the abscissa and the second number is the ordinate.

Exam Tip: Practice identifying coordinates correctly to avoid silly mistakes.

Question 8. Plot the following point on the number line using a graph and join the points. a) (3, -4) b) ( -3, 2)
Answer: Plot point \((3, -4)\) in the fourth quadrant and point \((-3, 2)\) in the second quadrant, then join them with a straight line segment.
In simple words: Plot both points on a Cartesian plane and draw a line connecting them.

Exam Tip: Use a sharp pencil and ruler for neat geometrical plotting.

Question 9. Which coordinates do the following points indicate?
Answer: Coordinates correspond to the labeled points A, B, C, D, E in the accompanying figure.
In simple words: Read the x and y values for each lettered point from the diagram.

Exam Tip: Always verify grid line intervals before reading coordinates.

Question 10. Plot the following coordinates on the Cartesian system : (2, 0), (-3, -4), (2, -2), (-4, 0), (-2, 3) and (1, 1.5).
Answer: Plot points \((2, 0)\), \((-3, -4)\), \((2, -2)\), \((-4, 0)\), \((-2, 3)\), and \((1, 1.5)\) on graph paper.
In simple words: Mark each given coordinate pair accurately on the Cartesian coordinate plane.

Exam Tip: For decimal coordinates like \(1.5\), plot halfway between 1 and 2 on the y-axis.

Question 11. Define the following:
a) The Cartesian plane
b) The coordinate axes
c) The Origin.
Answer:
a) The Cartesian plane: A plane formed by two perpendicular number lines (x-axis and y-axis) used to locate points.
b) The coordinate axes: The horizontal x-axis and vertical y-axis that intersect at right angles to form the reference system.
c) The Origin: The point of intersection \((0, 0)\) of the coordinate axes.
In simple words: These are the fundamental definitions of coordinate geometry used for plotting graphs.

Exam Tip: Learn exact definitions for scoring full marks in theory questions.