Question

Fill in the missing coordinates.

Answer 1

By the definition of midpoint, R is the midpoint of PQ hence PR is congruent to RQ. This would mean that the coordinates for Q are (0,4)

Answer 2

(4a, 0)

Explanation:

Looking at the graph, we can also say that the y-coordinate of Q is 0, as it lies on the x-axis. So we have (?,0), leaving us to find the x-coordinate.

Since the triangle is isoceles, we can assume that the x-coordinate 2a is the midpoint between PQ. If we draw a line from R perpendicular to PQ, it will cut PQ into two equal parts.

We can name this midpoint M, and this tells that the distance between P and M is equal to the distance between M and Q. The distance between P and M is 2a, and the distance between M and Q is equal, so that must mean both the distances are 2a. We add the distances together, and the total length of PQ is 4a.

The missing coordinate of Q is (4a,0)