Use the image to answer the question.

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:

$$\boxed{{\displaystyle 7}}$$