Question

Two similar triangles are shown on the coordinate grid:

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

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

The set of transformations has been performed on triangle ABC is dilation by a scale factor of 2 followed by reflection about the x-axis

Explanation:

Let us write the vertices of Δ ABC

∵ Vertex A = (-2, -1)

∵ Vertex B = (0, 0)

∵ Vertex C = (1, -3)

Let us Write the vertices of Δ A'B'C'

∵ Vertex A' = (-4, 2)

∵ Vertex B' = (0, 0)

∵ Vertex C' = (2, 6)

Let us find the scale factor k between the x-coordinates of the points and their images.

∵ -4 = k (-2) ⇒ Divide both side by -2

∵
`(-4)/(-2)` =
`(-2k)/(-2)`

∴ 2 = k

∴ The scale factor of a dilation is 2

∵ The signs of the y-coordinates of the images are the opposite of

the signs of the y-coordinates of the points

∴ The triangle is reflected about the x-axis

∴ The set of transformations has been performed on triangle ABC

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