Question

Suppose Q is the midpoint of segment PR, if PQ = x + 10, and QR = 4x - 2, what is the length of PR?

a) 25 units
b) 10 units
c) 14 units
d) 28 units

Answer 1

To find the length of PR, we can use the midpoint formula and set the x-coordinates and the y-coordinates equal to each other. Solving the resulting equation, we find that the length of PR is 14 units.

Step-by-step explanation:

To find the length of PR, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint are the average of the coordinates of the endpoints. In this case, the coordinates of Q (the midpoint) are

Q = ((P + R) / 2, ((P + R) / 2)

Since Q is the midpoint, we can set the x-coordinates and the y-coordinates equal to each other:

x + 10 = 4x - 2

Solving this equation for x, we get:

3x = 12

x = 4

Now, we can substitute x back into one of the expressions to find the length of PR. Let's use PQ = x + 10:

PQ = 4 + 10 = 14

Therefore, the length of PR is 14 units.