Chapter 1: Orienting Yourself: The Use of Coordinates

Exercise

Question

Question: 3 (i)

3 / 25

Consider the points R (3, 0), A (0, -2), M (-5, -2) and P (-5, 2). If they are joined in the same order, predict:

(i) Two sides of RAMP that are perpendicular to each other.

Now plot the points and verify your predictions.

Answer

1
Check the coordinates of the four points. Look for pairs of points that have the same x-coordinate or the same y-coordinate.
Points M and P have the same x-coordinate, -5. Therefore, MP is parallel to the y-axis.
Points A and M have the same y-coordinate, -2. Therefore, AM is parallel to the x-axis.
2
Check whether AM and MP meet at a common point. Then use their directions to determine whether they are perpendicular. Plot the points to verify your prediction.
Answer: The sides AM and MP are perpendicular.
Reason: AM is parallel to the x-axis, while MP is parallel to the y-axis. Since the x-axis and y-axis are perpendicular, AM and MP are also perpendicular. They meet at the common point M. The graph below verifies this prediction.
Coordinate graph showing points R, A, M, and P joined in order, with AM and MP forming a right angle at M.
Graph verifying that AM and MP are perpendicular.
Sponsored320 x 50