Question

Point M is the midpoint of segment QR. If QM = 16 + x and MR = 2(x + 2), find the length of QR. QR = 12 QR = -12 QR = 28 QR = 56

Answer 1

The midpoint divided a segment into two congruent lengths/segments.

So, QM = MR.

Set up the equation.

16 + x = 2(x+ 2)

16 + x = 2x + 4

12 + x = 2x

12 = x


Now, that you have the value of x, substitute it for the two equations.

QM = 16 + x

QM = 16 + 12

QM = 28


MR = 2(12+ 2)

MR = 2(14)

MR = 28


Find the whole length by of the line by adding the two segments. 28 × 2 = 56.

QR = 56