The dashed triangle is a dilation image of the solid triangle with the center at the origin. Is the dilation an enlargement or a reduction? Find the scale factor of the dilation.

Question

A solid triangle has vertices left parenthesis negative 6 comma 0 right parenthesis, left parenthesis 6 comma 3 right parenthesis, and left parenthesis 6 comma negative 6. A dashed triangle has vertices left parenthesis negative 2 comma 0 right parenthesis, left parenthesis 2 comma 1 right parenthesis, and left parenthesis 2 comma negative 2.

Answer 1

To determine whether the dilation is an enlargement or a reduction, we can compare the distances between corresponding points of the solid and dashed triangles.

Let's consider the distance between the first vertex of the solid triangle (-6, 0) and the first vertex of the dashed triangle (-2, 0). The distance between these two points is the absolute value of the difference of their x-coordinates: |-6 - (-2)| = |(-6) + 2| = |(-4)| = 4.

Now let's consider the distance between the second vertices: |6 - 2| = 4.

Finally, let's compare the distance between the third vertices: |(-6) - (-2)| = 4.

Since the distances between corresponding points are all equal, the dilation is an enlargement.

To find the scale factor of the dilation, we can compare the lengths of corresponding sides.

Let's compare the lengths of the sides formed by the first and second vertices: |(-6 - 6)|/|(-2 - 2)| = 12/4 = 3.

Now let's compare the lengths of the sides formed by the second and third vertices: |(6 - 6)|/|(2 - 2)| = 0/0 = undefined.

Since not all corresponding side lengths are equal, we cannot determine a single scale factor for the dilation. The scaling appears to be different for different sides.