)Two similar triangles are shown on the following 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′?

Comparing the points from the pre-image, ABC, to the image, A'B'C', we see that both x- and y-coordinates seem to be doubled from the pre-image to the image. However, the sign of the x-coordinates in the image is different; this means that the x-coordinates are negated. A reflection across the y-axis will negate the x-coordinates.

To double both the x- and y-coordinates, we would then apply a dilation by a factor of 2, as the scale factor gets multiplied by every coordinate.

deepakrai138 deepakrai138 · Answer 2 · 2022-01-04T06:32:25+01:00

The [tex]\Delta ABC[/tex] gets reflection across Y-axis and a dilation by a scale factor of 2.

Given,

The coordinates of [tex]\Delta ABC[/tex] are [tex]A(-3,2)[/tex], [tex]B(-1,0)[/tex] and [tex]C(-2,-1)[/tex] .

The coordinates of [tex]\Delta A'B'C'[/tex] are [tex]A'(6,4)[/tex], [tex]B'(2,0)[/tex] and [tex]C'(4,-2)[/tex] .

We have to find which transformation is performed on [tex]\Delta ABC[/tex] to form [tex]\Delta A'B'C'[/tex].

Now take a look on the coordinates of vertex of each triangle we found that each coordinate of [tex]\Delta A'B'C'[/tex] is doubled and the sign of abscissa of each coordinate of [tex]\Delta A'B'C'[/tex] is changed with respect to the coordinates of [tex]\Delta ABC[/tex].

Since the sign of abscissa of any coordinate of point is only changed when we reflect the point across Y-axis.

Hence the [tex]\Delta ABC[/tex] gets a reflection across Y-axis.

Since the coordinates of [tex]\Delta A'B'C'[/tex] gets doubled, so we can say that the [tex]\Delta ABC[/tex] gets dilated by a scale factor of 2.

Thus, the [tex]\Delta ABC[/tex] gets reflection across Y-axis and a dilation by a scale factor of 2.

For more on Reflection details follow the link:

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