Question

Given: PQ = 2x² + 10

QR = 14x - 2

Q is the midpoint of PR. Calculate the 2 possible lengths of QR.

A. QR = 12x - 12

B. QR = 16x - 12

C. QR = 14x + 8

D. QR = 18x - 12

Answer 1

To find the two possible lengths of QR, set up an equation using the fact that Q is the midpoint of PR. The two possible lengths of QR are 10 and 82. So, the correct answer is option A.

Step-by-step explanation:

To find the length of QR, we need to use the fact that Q is the midpoint of PR. This means that the lengths PQ and QR are equal. So, we set up an equation:

2x² + 10 = 14x - 2

2x² - 14x + 12 = 0

Next, we can solve this quadratic equation using factoring or the quadratic formula:

(x-2)(x-6) = 0

So, x = 2 or x = 6. Plugging these values back into the equation, we get two possible lengths for QR:

When x = 2, QR = 12 - 2 = 10

When x = 6, QR = 14(6) - 2 = 82

Therefore, the two possible lengths of QR are 10 and 82. So, the correct answer is option A.