OP Malhotra Class 9 Maths Solutions Chapter 20 Coordinates and Graphs of Simultaneous Linear Equations Exercise 20 (A)

S Chand Class 9 ICSE Maths Solutions Chapter 20 Coordinates and Graphs of Simultaneous Linear Equations Ex 20(A)

Question 1. Plot the following points on a graph paper using the same pair of axes and the same scale for each one.
(i) \( (0,18) \)
(ii) \( (2, 9) \)
(iii) \( (5, 8) \)
(iv) \( (7, 0) \)
(v) \( (5, -8) \)
(vi) \( (10,-16) \)
(vii) \( (8, -14) \)
(viii) \( (3,-11) \)
(ix) \( (-5, 6) \)
(x) \( (-15, 4) \)
(xi) \( (-20, 8) \)
(xii) \( (-9, 5) \)
(xiii) \( (-5, 8) \)
(xiv) \( (0, 7) \)
(xv) \( (-8, -15) \)
(xvi) \( (-12, -7) \)
(xvii) \( (-10, -11) \)
(xviii) \( (-8, 0) \)
(xix) \( (-4, 15) \)
(xx) \( (7, -6) \)
Answer: The points are plotted on the graph paper using the same axes and scale. Each point's location is determined by its x-coordinate (horizontal position) and y-coordinate (vertical position). For instance, \( (0, 18) \) is found by moving 0 units horizontally and 18 units up from the origin.
In simple words: To plot a point, start from the center (origin). Move right for positive x-values and left for negative x-values. Then, move up for positive y-values and down for negative y-values. Put a dot where you land.

🎯 Exam Tip: Always label your X and Y axes, mark the origin \( (0,0) \), and clearly indicate the scale used on both axes to avoid losing marks.

Question 2. The coordinates of the three vertices of a rectangle are given. By plotting the given points, find in each case, the coordinates of the fourth vertex.
(i) A \( (4, 2) \), B \( (-2, 2) \) and D \( (4, -2) \);
(ii) B \( (10, 4) \), C \( (0, 4) \) and D \( (0, -2) \).
Answer:
(i) The points A \( (4, 2) \), B \( (-2, 2) \) and D \( (4, -2) \) are plotted. To form a rectangle, the missing point C must have coordinates \( (-2, -2) \). This makes the opposite sides parallel to the axes and equal in length.
(ii) The points B \( (10, 4) \), C \( (0, 4) \) and D \( (0, -2) \) are plotted. To complete the rectangle, the fourth point A needs to be \( (10, -2) \). This point aligns with the existing B and D, maintaining the rectangular shape.
In simple words: For a rectangle with sides parallel to the axes, if you have three points, the fourth point will have the x-coordinate of one of the given points and the y-coordinate of another given point. Just look at the pattern of the given coordinates to find the missing one.

🎯 Exam Tip: When given three vertices of a rectangle, visualize or sketch the points. The fourth vertex will complete the parallel sides, meaning its coordinates will match one x-coordinate and one y-coordinate from the adjacent vertices.

Question 3. A \( (-2, 4) \), C \( (4, 10) \) and D \( (-2, 10) \) are the vertices of a square ABCD. Use graphical method to find the coordinates of the fourth vertex B. Also, find
(i) the coordinates of the mid-point of BC,
(ii) the coordinates of the mid-point of CD and
(iii) the coordinates of the point of intersection of the diagonals of the square ABCD.
Answer: First, we plot the given points A \( (-2, 4) \), C \( (4, 10) \), and D \( (-2, 10) \) on a graph. By joining these points and completing the square, we find the coordinates of the fourth vertex.
(i) The fourth vertex B is located at \( (4, 4) \).
(ii) The mid-point of BC, labeled as P, has coordinates \( (4, 7) \).
(iii) The mid-point of CD, labeled as Q, has coordinates \( (1, 10) \).
(iv) The diagonals AC and BD meet each other at point O, and its coordinates are \( (1, 7) \). This point is also the center of the square.

In simple words: When you have three points of a square, plot them. The fourth point will complete the shape, making all sides equal and angles 90 degrees. Midpoints are found halfway along each side. Diagonals cross at the exact center of the square.

🎯 Exam Tip: Remember that in a square, opposite sides are parallel and equal, and diagonals bisect each other at their midpoint. This helps in finding missing vertices or intersection points.