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

x=−13
x equals negative 13

x=7
x equals 7

x=176

Answer 1

In a rectangle, the diagonals bisect each other. Therefore, segments \( AO \) and \( BO \) must be equal in length at point \( O \).

Set the expressions for segments \( AO \) and \( BO \) equal to each other:

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

Now, solve for \( x \):

1. Subtract \( 4x \) from both sides:

\[
-3 = x - 10
\]

2. Add \( 10 \) to both sides:

\[
7 = x
\]

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

\[
\boxed{7}
\]