Maharashtra Board Class 9 Maths Part 2 Geometry Chapter 7 Set 7.1 Co ordinate Solutions

Question 1. State in which quadrant or on which axis do the following points lie.
(i) A(-3, 2)
(ii) B(-5, -2)
(iii) K(3.5, 1.5)
(iv) D(2, 10)
(V) E(37, 35)
(vi) F(15, -18)
(vii) G(3, -7)
(viii) H(0, -5)
(ix) M(12, 0)
(x) N(0, 9)
(xi) P(0, 2.5)
(xii) Q(-7, -3)
Answer:

In simple words: The quadrant or axis a point lies on is determined by the signs of its x and y coordinates. Positive x and y is Quadrant I, negative x and negative y is Quadrant III, positive x and negative y is Quadrant IV, and negative x and positive y is Quadrant II. Points with a zero coordinate lie on an axis.

🎯 Exam Tip: Understanding the coordinate system and the sign conventions for each quadrant is crucial for accurately locating points and is a fundamental skill in coordinate geometry.

Question 2. In which quadrant are the following points?
(i) whose both co-ordinates are positive.
(ii) whose both co-ordinates are negative.
(iii) whose x co-ordinate is positive and the y co-ordinate is negative.
(iv) whose x co-ordinate is negative and y co-ordinate is positive.
Answer:
(i) Quadrant I
(ii) Quadrant III
(iii) Quadrant IV
(iv) Quadrant II
In simple words: The location of a point in a Cartesian plane (Quadrant I, II, III, or IV) is defined by the unique combination of positive or negative signs of its x and y coordinates.

🎯 Exam Tip: Memorizing the sign conventions for x and y coordinates in each of the four quadrants is essential for quickly determining a point's location.

Question 3. Draw the co-ordinate system on a plane and plot the following points.
L(-2, 4), M(5, 6), N(-3, -4), P(2, -3), Q(6, -5), S(7, 0), T(0, -5)
Answer:
ℹ️ चित्र व्याख्या (Diagram Explanation): यह आरेख एक कार्तीय निर्देशांक प्रणाली को दर्शाता है जिसमें X और Y अक्ष, एक मूलबिंदु (0,0), और दोनों अक्षों पर 1 सेमी = 1 इकाई का पैमाना है। इसमें कई बिंदुओं को दर्शाया गया है: L(-2, 4), M(5, 6), N(-3, -4), P(2, -3), Q(6, -5), S(7, 0), और T(0, -5)। ग्रिड रेखाएं छात्रों को बिना किसी कठिनाई के प्रत्येक बिंदु की सटीक स्थिति को समझने में मदद करती हैं, चाहे वे संबंधित चतुर्थांश में हों या अक्षों पर।
In simple words: To plot points, draw perpendicular lines from the x-coordinate on the X-axis and the y-coordinate on the Y-axis; their intersection is the point. Points on an axis have one coordinate as zero.

🎯 Exam Tip: Accuracy in drawing axes, marking scales, and precisely locating points is critical. Use a ruler and graph paper for the best results to avoid errors in plotting.

Maharashtra Board Class 9 Maths Chapter 7 Co-Ordinate Geometry Practice Set 7.1 Intext Questions And Activities

Question 1. Plot the points R(-3,-4), S(3,-1) on the same co-ordinate system. (Textbook pg. no. 93)
Steps for plotting the points:
(i) Draw X-axis and Y-axis on the plane. Show the origin.
(ii) Draw a line parallel to Y-axis at a distance of 3 units in the -ve direction of X-axis.
(iii) Draw another line parallel to X-axis at a distance of 4 units in the -ve direction of Y-axis.
(iv) Intersection of these lines is the point R (-3, -4).
(v) The point S can be plotted in the same manner.
Answer:
ℹ️ चित्र व्याख्या (Diagram Explanation): यह आरेख एक कार्तीय निर्देशांक प्रणाली को दर्शाता है जिसमें X और Y अक्ष, एक मूलबिंदु (0,0), और दोनों अक्षों पर 1 सेमी = 1 इकाई का पैमाना है। इसमें दो विशिष्ट बिंदु, R(-3, -4) और S(3, -1) दर्शाए गए हैं। बिंदु R तीसरे चतुर्थांश में स्थित है, और बिंदु S चौथे चतुर्थांश में स्थित है, जिसमें ग्रिड रेखाएं उनके सटीक निर्देशांक दर्शाती हैं।
In simple words: To plot a point, you move along the X-axis by its x-coordinate value and then move parallel to the Y-axis by its y-coordinate value from that position.

🎯 Exam Tip: Always label the axes, origin, and scale on your coordinate system. Clearly mark and label each plotted point to ensure full marks for accuracy.