Question

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

Answer 1

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

$(x,y)\rightarrow (kx,ky)$

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

$(x,y)\rightarrow (2x,2y)$

The vertices of triangle ABC after dilation are

$A(-3,2)\rightarrow A_1(-6,4)$

$B(-1,0)\rightarrow B_1(-2,0)$

$C(-2,-1)\rightarrow C_1(-4,-2)$

If a figure reflected across y-axis, then

$(x,y)\rightarrow (-x,y)$

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

$A_1(-6,4)\rightarrow A'(6,4)$

$B_1(-2,0)\rightarrow B'(2,0)$

$C_1(-4,-2)\rightarrow C'(4,-2)$

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.

Answer 2

Answer:

its D i just did the test have a great day

Step-by-step explanation: