Question

Use the image to answer the question.

Parallelogram upper M upper N upper O upper P is shown with base upper O upper P larger than height upper N upper O. Diagonals are drawn from upper M to upper O and upper N to upper P to meet at upper L.

In parallelogram MNOP
, the diagonals MO
and NP
intersect at point L
. ML=x+7
and LO=2x−10
. What is the value of x?

(1 point)
Responses

x=17
x equals 17

x=−7
x equals negative 7

x=24
x equals 24

x=−3

Answer 1

In a parallelogram, the diagonals bisect each other. This means that the lengths of segments from the intersection point \( L \) to the ends of each diagonal should be equal.

Given:
- \( ML = x + 7 \)
- \( LO = 2x - 10 \)

Since \( ML \) and \( LO \) are segments of the diagonals that intersect at point \( L \), we can set them equal to each other:

\[
ML = LO
\]

Substituting the expressions:

\[
x + 7 = 2x - 10
\]

Now we can solve for \( x \). First, let's get all the \( x \) terms on one side and the constant terms on the other side:

\[
7 + 10 = 2x - x
\]

This simplifies to:

\[
17 = x
\]

So, the value of \( x \) is:

\[
x = 17
\]

The correct response is:

x=17