Question

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


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=−425

x equals negative Start Fraction 42 over 5 End Fraction

x=−3

x equals negative 3

x=3

x equals 3

x=−214

Answer 1

O is the intersection of the diagonals, so the diagonals bisect each other. Thus CO = (1/2)BD.

Set up equation: -3x = (1/2)(x + 21).
Multiply by 2: -6x = x + 21 → -7x = 21 → x = -3.

Answer: x = -3.