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
1 answer
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 \( x \):
\[ -3 = x - 10 \]
\[ 7 = x \]
Therefore, the value of \( x \) is:
\[ \boxed{7} \]
