Question

Reflect triangle ABC over the line y = 2.

Translate the image by the directed line segment from (0, 0) to (3, 2).

What are the coordinates of the vertices in the final image?

Answer 1

The question is an illustration of transformation, and the coordinates of the image of the triangle are (-3,7), (-2,4) and (0,6)

How to transform the triangle?

The coordinates of the triangle are given as:

(-6,-1), (-5,2) and (-3,0)

When the triangle is reflected across the line y = 2 is, the new points are

(-6,5), (-5,2) and (-3,4)

Next, we translate the image of the triangle using the translation

(x,y) -> (x + 3, y +2)

So, we have:

(-6,5) => (-6 + 3, 5 + 2) = (-3,7)

(-5,2) => (-5 + 3, 2 + 2) = (-2,4)

(-3,4) => (-3 + 3, 4 + 2) = (0,6)

Hence, the coordinates of the image of the triangle are (-3,7), (-2,4) and (0,6)

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