Question

Parallelogram CARD has vertices (5, -2), (-1, -2), (1, 2), and (7, 2), respectively. The diagonals, CR and AD intersect at Point T. What is the length of CT? What is the length of DT?

Answer 1

HI

Line segment DT is 4.47 units
and line segment CT is 2.83 units

BYE

Answer 2

CT = DT = 4 units.

Explanation:

The diagonals of a parallelogram bisect each other, this means that the point of intersection is the midpoint for each one of them.

So, diagonal CR has coordinates C(5,-2) and R(1,2). Its midpoint would be

`x_(m)=(x_(1) +x_(2) )/(2)=(5+1)/(2)=3\\y_(m)=(-2+2)/(2)=0`

Therefore, the mid point is at (3,0).

Now, to find the length of CT and DT, we use the definition of distance between two points:

`d=\sqrt{(x_(2)-x_(1))^(2) +(y_(2)-y_(1))^(2) }\\d=\sqrt{(5-3)^(2) +(-2-0)^(2) }=√(4+4)=√(16)\\  d=4`

Therefore, the length of CT is 4 units. DT has the same length, because as we said, T divides diagonal is equal parts because is a mid point.

So, CT = DT = 4 units.