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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=7
x equals 7

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

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

x=−13

1 answer

In a rectangle, the diagonals bisect each other, meaning that the lengths of segments AO and BO should be equal at the intersection point O.

We are given:

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

Setting these two expressions equal to each other gives us the equation:

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

To solve for \( x \), we can first subtract \( 4x \) from both sides:

\[ -3 = x - 10 \]

Next, we add \( 10 \) to both sides:

\[ 7 = x \]

Thus, the value of \( x \) is \( 7 \).

So, the correct response is:

x=7