Question

triangle midsegment (algebraic)
score: 1/5 penalty: 0.25 off
question
in the diagram below of triangle nop, q is the mid - point of $overline{np}$ and r is the mid - point of $overline{op}$. if $qr=-23 + 8x$, and $no=-3x + 49$, what is the measure of $overline{qr}$?
answer attempt 1 out of 2
$qr=$

Explanation:

Step1: Apply mid - segment theorem

By the triangle mid - segment theorem, $QR=\frac{1}{2}NO$. So, $- 23 + 8x=\frac{1}{2}(-3x + 49)$.

Step2: Multiply both sides by 2

$2(-23 + 8x)=-3x + 49$.
$ - 46+16x=-3x + 49$.

Step3: Add 3x to both sides

$-46 + 16x+3x=-3x + 49+3x$.
$-46 + 19x=49$.

Step4: Add 46 to both sides

$-46+46 + 19x=49 + 46$.
$19x=95$.

Step5: Solve for x

$x = 5$.

Step6: Find the measure of QR

Substitute $x = 5$ into the expression for $QR$: $QR=-23+8\times5=-23 + 40=13$.

Answer:

13