Two similar triangles are shown on the coordinate grid:

A coordinate plane is shown. Triangle ABC has vertices A at negative 3 comma 2, B at negative 1 comma 0, and C at negative 2 comma negative 1. Triangle A prime B prime C prime has vertices A prime at 6 comma 4, B prime at 2 comma 0, and C prime at 4 comma negative 2.

Which set of transformations has been performed on triangle ABC to form triangle A′B′C′? (4 points)

Dilation by a scale factor of 4 followed by reflection about the x-axis

Dilation by a scale factor of 2 followed by reflection about the x-axis

Dilation by a scale factor of 4 followed by reflection about the y-axis

Dilation by a scale factor of 2 followed by reflection about the y-axis

Question

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Respuesta :

erinna erinna · Answer 1 · 2019-11-01T12:21:21+01:00

Answer:

Option D.

Step-by-step explanation:

The vertices of triangle ABC are A(-3,2), B(-1,0), C(-2,-1).

The vertices of triangle A'B'C' are A'(6,4), B'(2,0) and C'(4,-2).

If a figure dilated by a scale factor of k and center of dilation is (0,0), then

[tex](x,y)\rightarrow (kx,ky)[/tex]

The triangle ABC dilated by a scale factor of 2, so

[tex](x,y)\rightarrow (2x,2y)[/tex]

The vertices of triangle ABC after dilation are

[tex]A(-3,2)\rightarrow A_1(-6,4)[/tex]

[tex]B(-1,0)\rightarrow B_1(-2,0)[/tex]

[tex]C(-2,-1)\rightarrow C_1(-4,-2)[/tex]

If a figure reflected across y-axis, then

[tex](x,y)\rightarrow (-x,y)[/tex]

So, the vertices of triangle after dilation followed by reflection are

[tex]A_1(-6,4)\rightarrow A'(6,4)[/tex]

[tex]B_1(-2,0)\rightarrow B'(2,0)[/tex]

[tex]C_1(-4,-2)\rightarrow C'(4,-2)[/tex]

The required set of transformation is "Dilation by a scale factor of 2 followed by reflection about the y-axis"

Therefore, the correct option is D.

baynesharp baynesharp · Answer 2 · 2021-06-17T19:24:47+02:00

baynesharp baynesharp

Answer:

its D i just did the test have a great day

Step-by-step explanation:

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