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

Answer:

CT = DT = 4 units.

Step-by-step 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

$x_{m}=\frac{x_{1} +x_{2} }{2}=\frac{5+1}{2}=3\\y_{m}=\frac{-2+2}{2}=0$

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:

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

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.