Answer:
a) T(3,0)
b) |CT|=2.83
c) |DT|=4.47
Step-by-step explanation:
The given parallelogram CARD has vertices (5, -2), (-1, -2), (1, 2), and (7, 2)
The diagonals of a parallelogram bisect each other.
Find the midpoint of one diagonal, that gives us the point of intersection of the diagonals T.
The midpoint of C(5,-2) and (1,2) is
![T(\frac{5+1}{2},\frac{-2+2}{2} )](https://tex.z-dn.net/?f=T%28%5Cfrac%7B5%2B1%7D%7B2%7D%2C%5Cfrac%7B-2%2B2%7D%7B2%7D%20%20%29)
![T(3,0)](https://tex.z-dn.net/?f=T%283%2C0%29)
b) To find the length of CT, we use the distance formula; where C(5,-2) ahd T(3,0).
![d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
![d=\sqrt{(3-5)^2+(-2-0)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%283-5%29%5E2%2B%28-2-0%29%5E2%7D)
![d=\sqrt{4+4}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B4%2B4%7D)
![d=\sqrt{8}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B8%7D)
![d=2\sqrt{2}=2.83](https://tex.z-dn.net/?f=d%3D2%5Csqrt%7B2%7D%3D2.83)
The length of CT is 2.83 to the nearest hundredth
c) To find the length of DT, we use the distance formula; where D(7,2) ahd T(3,0).
![d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
![d=\sqrt{(3-7)^2+(2-0)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%283-7%29%5E2%2B%282-0%29%5E2%7D)
![d=\sqrt{16+4}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B16%2B4%7D)
![d=\sqrt{20}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B20%7D)
![d=2\sqrt{5}=4.47](https://tex.z-dn.net/?f=d%3D2%5Csqrt%7B5%7D%3D4.47)
The length of DT is 4.47 to the nearest hundredth