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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)

Respuesta :

MrRoyal

Answer:

Triangle Z

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.

[tex]C = (2,-1), (2,2), (1,-1)[/tex]

[tex]Z = (4, - 2), (4, 4), (2, - 2)[/tex]

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

[tex]Scale\ Factor = \frac{Z}{C}[/tex]

For [tex]C = (2,-1)[/tex] and [tex]Z = (4, - 2[/tex]

[tex]Scale\ Factor = \frac{(4,-2)}{(2,-1)}[/tex]

Factorize:

[tex]Scale\ Factor = \frac{2(2,-1)}{(2,-1)}[/tex]

[tex]Scale\ Factor = 2[/tex]

For [tex]C = (2,2)[/tex] and [tex]Z = (4, 4)[/tex]

[tex]Scale\ Factor = \frac{(4,4)}{(2,2)}[/tex]

Factorize:

[tex]Scale\ Factor = \frac{2(2,2)}{(2,2)}[/tex]

[tex]Scale\ Factor = 2[/tex]

Lastly;

[tex]C = (1,-1)[/tex]

[tex]Z =(2, - 2)[/tex]

[tex]Scale\ Factor = \frac{(2,-2)}{(1,-1)}[/tex]

Factorize:

[tex]Scale\ Factor = \frac{2(1,-1)}{(1,-1)}[/tex]

[tex]Scale\ Factor = 2[/tex]

Notice that the scale factor is the same all through.

Hence, Z is similar to C