Question

Describe the transformations that will map triangle A to triangle B and illustrate the similarity between the two triangles. A) rotate 90° clockwise and then translate 6 units down B) translate 4 units down and rotate 180° about the origin C) reflect the triangle across the y-axis and translate 4 units down D) reflect triangle A across the x-axis and then translate 1 unit right

Answer 1

B) Translate 4 units down and rotate 180°

Rule for 180° = (x, y) ---- (-x, -y)

Pick one point on Triangle A. (I picked the pointiest point)

(-5, 6)

Now translate 4 units down.

You will now be on (-5, 2)

Rotate 180°

You will now have (5, -2)

And the pointiest point on Triangle B is (5, -2)

So, B is the correct answer.

Answer 2

Option B is correct. The required transformation that will map triangle A to triangle B and illustrate the similarity between the two triangles is translating 4 units down and rotate 180° about the origin

In order to determine the transformation that will map triangle A to B, we need to do the following:

• Select any of the coordinates of the vertices

• Using the coordinate point (-5, 6) on triangle A

• If a coordinate (x, y)  is rotated 180° about the origin, the resulting coordinate will be at (-x, -y)

• For the coordinate (-5, 6), rotated 180° about the origin, the resulting coordinate will be at (5, -6)

If the coordinate is translated 4 units down as seen from the figure, the resulting coordinate of the vertex on triangle B will be at (5, -6+4) i.e. (5, -2)

We can see that it tallies with a similar coordinate on triangle B. Hence the required transformation that will map triangle A to triangle B and illustrate the similarity between the two triangles is translating 4 units down and rotate 180° about the origin

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