Question

Use the image to answer the question.

A rectangle upper A upper B upper C upper D has diagonals between upper A upper C and upper B upper D. The diagonals insect at upper O, in the center. Segment upper A upper O is labeled 4 x minus 3. Segment upper B upper O is labeled 5 x minus 10.

Given that ABCD
is a rectangle with AO=4x−3
and BO=5x−10
, what is the value of x?

(1 point)
Responses

x=176
x equals Start Fraction 17 over 6 End Fraction

x=7
x equals 7

x=−43
x equals negative Start Fraction 4 over 3 End Fraction

x=−13

Answer 1

In a rectangle, the diagonals are equal in length. Therefore, the lengths of segments \( AO \) and \( BO \) must be equal.

Given:
- \( AO = 4x - 3 \)
- \( BO = 5x - 10 \)

Setting these two expressions equal to each other gives us:

\[
4x - 3 = 5x - 10
\]

To solve for \( x \), we can first move all terms involving \( x \) to one side and the constant terms to the other side:

\[
4x - 5x = -10 + 3
\]

This simplifies to:

\[
-x = -7
\]

Multiplying both sides by -1 yields:

\[
x = 7
\]

Thus, the value of \( x \) is \( 7 \). The correct answer is:

**x = 7**.