The triangle ACE, is a dilation image of triangle ABD. Point A is the center of dilation. Tell whether the dilation is an enlargement or a reduction. Then find the scale factor of the dilation.
The length of side AC is 10.
To determine whether the dilation is an enlargement or a reduction, we need to compare the lengths of corresponding sides of the two triangles.
Given that side AC of triangle ACE is 10, and point A is the center of dilation, we can compare the corresponding sides of triangle ACE and triangle ABD:
AC corresponds to AB in triangle ABD.
If AC = 10 and AB = x, then we can find the scale factor as follows:
Scale factor = AC / AB
Scale factor = 10 / x
Since we are comparing lengths of corresponding sides, the scale factor will give us the ratio of the lengths of the sides in the two triangles.
If the scale factor is greater than 1, the dilation is an enlargement. If the scale factor is less than 1, the dilation is a reduction.
Once the length of side AB is known, we can find the scale factor of the dilation.
the side is 8
Given that side AC is 10 and side AB is 8, we can now find the scale factor of the dilation:
Scale factor = AC / AB
Scale factor = 10 / 8
Scale factor = 5 / 4
Since the scale factor is greater than 1 (1.25), the dilation is an enlargement.
Therefore, the scale factor of the dilation is 5/4 or 1.25.