he dashed-line triangle is a dilation image of the solid-lined triangle.
graph
A triangle formed by solid black line segments is shown with vertices at negative 4 comma 8, negative 4 comma 2, and 4 comma 2.
A second larger triangle formed by dashed line segments is shown with vertices at negative 9 comma 4, negative 9 comma negative 8, and 7 comma negative 8.
Is the dilation an enlargement or a reduction? What is the scale factor of the dilation?
To determine whether the dilation is an enlargement or a reduction and to find the scale factor, we need to compare the sizes of the corresponding sides of the two triangles. By finding the ratio of the lengths of the sides of the dashed-line triangle to the solid-lined triangle, we can determine the scale factor.
First, we need to calculate the lengths of the sides of the original solid-lined triangle. For simplicity, let's call the vertices of the solid-lined triangle A (-4, 8), B (-4, 2), and C (4, 2). We'll do the same for the vertices of the dashed-line triangle, calling them A' (-9, 4), B' (-9, -8), and C' (7, -8).
The side AB of the solid-lined triangle is vertical, so its length is the difference in the y-coordinates of A and B:
Length AB = |8 - 2| = 6
The corresponding side A'B' of the dashed-line triangle is also vertical:
Length A'B' = |4 - (-8)| = |4 + 8| = 12
Now, let's find the ratio of the lengths of A'B' to AB to determine the scale factor (k):
k = Length A'B' / Length AB = 12 / 6 = 2
Since k > 1, the dilation is an enlargement, and the scale factor of the dilation is 2.