Question

Which triangle defined by the given points on the coordinate plane is similar to the triangle illustrated

Answer 1

the answer is c

Explanation:

Answer 2

Option D.

Explanation:

The vertices of given triangle are (2,-2), (5,-2) and (2,2).

Distance formula:

`D=√((x_2-x_1)^2+(y_2-y_1)^2)`

Using distance formula, the length of sides of given triangle are

`√(\left(5-2\right)^2+\left(-2-\left(-2\right)\right)^2)=3`

`√(\left(2-5\right)^2+\left(2-\left(-2\right)\right)^2)=5`

`√(\left(2-2\right)^2+\left(2-\left(-2\right)\right)^2)=4`

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

`√(\left(8-2\right)^2+\left(-2-\left(-2\right)\right)^2)=6`

`√(\left(2-8\right)^2+\left(6-\left(-2\right)\right)^2)=10`

`√(\left(2-2\right)^2+\left(6-\left(-2\right)\right)^2)=8`

It is noticed that

`(6)/(3)=(10)/(5)=(8)/(4)=2`

Since the sides of given triangle and side of triangle in option D are proportional. Therefore, the correct option is D.