Question

Triangle C has vertices (2, – 1), (2, 2), and (1, -1).

NEED HELP ASAP
Which triangle is similar to triangle C?
0 Triangle X with vertices (-2, 2), (2, 4), and (1,2)
o Triangle Y with vertices (4, 1), (2, 3), and (2, 2)
o Triangle Z with vertices (4, - 2), (4, 4), and (2, - 2)
o Triangle W with vertices (4, – 3), (4, 0), and (2. – 3)

Answer 1

Triangle Z

Step-by-step explanation:

Required

Similar triangle to triangle C

Similar triangles do not necessarily have the same size. However, they must be in proportion of size and their angles must be equal.

From the list of options given, triangle Z is a dilation of C and this is shown below.

`C = (2,-1), (2,2), (1,-1)`

`Z = (4, - 2), (4, 4), (2, - 2)`

Divide the corresponding coordinates of Z by C to get the scale factor.

`Scale\ Factor = (Z)/(C)`

For
`C = (2,-1)` and
`Z = (4, - 2`

`Scale\ Factor = ((4,-2))/((2,-1))`

Factorize:

`Scale\ Factor = (2(2,-1))/((2,-1))`

`Scale\ Factor = 2`

For
`C = (2,2)` and
`Z = (4, 4)`

`Scale\ Factor = ((4,4))/((2,2))`

Factorize:

`Scale\ Factor = (2(2,2))/((2,2))`

`Scale\ Factor = 2`

Lastly;

`C = (1,-1)`

`Z =(2, - 2)`

`Scale\ Factor = ((2,-2))/((1,-1))`

Factorize:

`Scale\ Factor = (2(1,-1))/((1,-1))`

`Scale\ Factor = 2`

Notice that the scale factor is the same all through.

Hence, Z is similar to C