Which triangle defined by the given points on the coordinate plane is similar to the triangle illustrated?
A) (-1,1),(-1,4),(-6,1)
B) (-1,1),(-1,5),(-6,1)
C) (-1,1),(-1,4),(-7,1)
D) (-1,1),(-1,5),(-7,1)

D)(-1,1),(-1,5),(-7,1)

Step-by-step explanation:

The vertices of the triangle shown in the coordinate plane are: (-1,1), (-1,3), (-4,1)

The legs are in the ratio:2 : 3

For triangle with vertices A)(-1,1),(-1,4),(-6,1),

The legs are in the ratio: 3:5

For triangle with vertices:

B)(-1,1),(-1,5),(-6,1)

The legs are in the ratio:

4:5

For the triangle with vertices:

C)(-1,1),(-1,4),(-7,1)

The legs are in the ratio:

3:6=1:2

For triangle with vertices:

D)(-1,1),(-1,5),(-7,1)

The legs are in the ratio:

4:6=2:3

Therefore the correct answer is D.

Because similar triangles have their corresponding sides in the same proportion.