Question

On the number line shown below, point M is the midpoint of PQ. What number is located at point Q?

P M Q
<----o------------o------------o---->
-2 5

Answer 1

The coordinates of point Q are: (4, 10).

Given point M is the midpoint of PQ, which means it divides the line segment PQ into two segments of equal length. Let's denote the coordinates of point P as (p_x, p_y) and the coordinates of point Q as (q_x, q_y). Since the midpoint M divides PQ into two segments of equal length, we can use the midpoint formula to find the coordinates of M:

M_x = (p_x + q_x) / 2

M_y = (p_y + q_y) / 2

We are given that the midpoint M is located at (-2, 5). Therefore, we can substitute these values into the midpoint formula:

-2 = (p_x + q_x) / 2

5 = (p_y + q_y) / 2

Solving for p_x and q_x, we get:

p_x = -8

q_x = 4

Solving for p_y and q_y, we get:

p_y = 0

q_y = 10

Therefore, the coordinates of point Q are (4, 10).