Answer:
Option D.
Step-by-step explanation:
The vertices of given triangle are (2,-2), (5,-2) and (2,2).
Distance formula:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using distance formula, the length of sides of given triangle are
[tex]\sqrt{\left(5-2\right)^2+\left(-2-\left(-2\right)\right)^2}=3[/tex]
[tex]\sqrt{\left(2-5\right)^2+\left(2-\left(-2\right)\right)^2}=5[/tex]
[tex]\sqrt{\left(2-2\right)^2+\left(2-\left(-2\right)\right)^2}=4[/tex]
The sides of similar triangles are proportional.
Similarly, find the sides for each option.
The vertices of option D are
(2,-2), (8,-2), (2,6)
Using distance formula, the length of sides of this triangle are
[tex]\sqrt{\left(8-2\right)^2+\left(-2-\left(-2\right)\right)^2}=6[/tex]
[tex]\sqrt{\left(2-8\right)^2+\left(6-\left(-2\right)\right)^2}=10[/tex]
[tex]\sqrt{\left(2-2\right)^2+\left(6-\left(-2\right)\right)^2}=8[/tex]
It is noticed that
[tex]\dfrac{6}{3}=\dfrac{10}{5}=\dfrac{8}{4}=2[/tex]
Since the sides of given triangle and side of triangle in option D are proportional. Therefore, the correct option is D.
