Question

Use the image to answer the question.

Rectangle upper A upper B upper C upper D is shown with point upper O in the center. Diagonal segments upper A upper C and upper B upper D intersect at point upper O, in the center of the rectangle. Some line segments have measurements.

Image Long DescriptionSegment upper C upper O is labeled negative 3 x. Segment upper B upper D is labeled x plus 21.

The rectangle ABCD
is given as shown. Find x if CO=−3x
and BD=x+21
.

(1 point)
Responses

x=−3
x equals negative 3

x=−425
x equals negative Start Fraction 42 over 5 End Fraction

x=−214
x equals negative Start Fraction 21 over 4 End Fraction

x=3
x equals 3
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Answer 1

In a rectangle the diagonals are equal and bisect each other, so BD = AC = 2·CO. Thus
x + 21 = 2(−3x) = −6x.
Solve: x + 21 = −6x → 7x = −21 → x = −3.

Answer: x = −3.