The dashed-line triangle is a dilation image of the solid-lined triangle.
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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?
(1 point)
Responses
reduction; 1/2
reduction; Image with alt text: 1/2
enlargement; 2
enlargement; 2
reduction; 2
reduction; 2
enlargement; 1/2
To determine whether the dilation is an enlargement or a reduction, we can compare the sizes of the two triangles. By looking at their coordinates, we can calculate the distances between corresponding points and determine the scale factor.
For the solid-lined triangle, let's look at the vertical distance between the vertices at (-4, 8) and (-4, 2), which is 8 - 2 = 6 units.
Now, let's look at the corresponding vertices of the dashed-line triangle at (-9, 4) and (-9, -8), which have a vertical distance of 4 - (-8) = 12 units.
Since the distance in the dashed-line triangle is twice the distance in the solid-lined triangle, the scale factor is 12 / 6 = 2.
Therefore, the dilation is an enlargement with a scale factor of 2.
The correct answer is:
enlargement; 2