openstudy(.)com/updates/attachments/514a5d2ae4b05e69bfac38d2-mimisilly-1363828099165-ikk.png
The dashed triangle is a dilation image of the solid triangle with the center at the origin. Is the dilation a enlargement or reduction? Find the scale factor.
I know this is a reduction but I'm not so sure about the scale factor... I believe it is 3?
Yes, you are correct. The dashed triangle is a reduction of the solid triangle, and the scale factor is 3.
To determine whether the dilation is an enlargement or a reduction, we can examine the sizes of the corresponding sides. If the corresponding sides become smaller, it is a reduction; if they become larger, it is an enlargement.
Now, let's analyze the image you provided:
From the solid triangle to the dashed triangle, all the corresponding sides have decreased in length. Therefore, it is indeed a reduction.
To find the scale factor, we can compare the lengths of corresponding sides. Let's focus on one pair of corresponding sides, such as the base of the solid triangle and the corresponding side of the dashed triangle.
In the solid triangle, the length of the base is 8 units. In the dashed triangle, the length of the corresponding side is 2 units. To find the scale factor, we can divide the length of the corresponding side of the dashed triangle by the length of the base of the solid triangle:
Scale factor = Length of corresponding side of dashed triangle / Length of base of solid triangle
Scale factor = 2 units / 8 units
Scale factor = 1/4
Therefore, the scale factor is 1/4.
To determine whether the dilation is an enlargement or a reduction, we can compare the size of the dashed triangle to the solid triangle. If the dashed triangle is smaller than the solid triangle, it is a reduction.
Looking at the image in the link you provided, it is clear that the dashed triangle is indeed smaller than the solid triangle. Therefore, the dilation is a reduction.
To find the scale factor, we can compare the corresponding sides of the solid triangle and the dashed triangle. Let's denote the length of a side of the solid triangle as "x," and the corresponding length of the dashed triangle as "y."
From the image, we can observe that the length of the side of the solid triangle is 9 units, and the length of the corresponding side of the dashed triangle is 3 units.
So, the scale factor can be calculated as follows:
Scale factor = length of corresponding side in the dashed triangle / length of corresponding side in the solid triangle
Scale factor = y / x
Scale factor = 3 / 9
Simplifying, we get:
Scale factor = 1 / 3
Therefore, the scale factor of the dilation is 1/3, indicating that the dashed triangle is one-third the size of the solid triangle.