Question

What sequence of transformations, when applied to △ABC , shows that ​ ​ △ABC ​ ​ is similar to △ A ′ B ′ C ′ ? dilation with respect to the origin by a scale factor of 2 followed by a translation of 2 units left dilation with respect to the origin by a scale factor of 1 2 followed by a translation of 2 units right translation of 2 units right followed by a dilation with respect to the origin by a scale factor of 1 2 translation of 2 units left followed by a dilation with respect to the origin by a scale factor of 1 2

Answer 1

The correct sequence of transformations that shows that △ABC is similar to △A′B′C′ is:

translation of 2 units left followed by a dilation with respect to the origin by a scale factor of 12.

Explanation:

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object.

In this case, we can see that a dilation with respect to the origin by a scale factor of 12 would stretch or shrink the triangle, but would not change the angles.

Therefore, we need to apply a translation first to move the triangle into the correct position.

So, we first translate the triangle 2 units left, which does not change its shape or size, but moves it to a position where it can be more easily compared to the other triangle.

Then, we apply a dilation with respect to the origin by a scale factor of 12, which stretches or shrinks the triangle but does not change its shape.