Describe the dilation of triangle ABC%0D%0A%0D%0A%0D%0A%0D%0A , with a scale factor of 5 and a center point of dilation at the origin (0, 0)%0D%0A(%0D%0A0%0D%0A,%0D%0A %0D%0A0%0D%0A)%0D%0A . %0D%0AResponses%0D%0A%0D%0ATriangle A′B′C′%0D%0A%0D%0A′%0D%0A%0D%0A′%0D%0A%0D%0A′%0D%0A is 5 times as large as triangle ABC%0D%0A%0D%0A%0D%0A%0D%0A and is 5 times closer to the center point of dilation.%0D%0A Triangle cap A prime cap b prime cap c prime is 5 times as large as triangle cap A cap b cap c and is 5 times closer to the center point of dilation. - no response given%0D%0A%0D%0ATriangle A′B′C′%0D%0A%0D%0A′%0D%0A%0D%0A′%0D%0A%0D%0A′%0D%0A is 5 times smaller than triangle ABC%0D%0A%0D%0A%0D%0A%0D%0A and is 5 times as far from the center point of dilation.%0D%0A Triangle cap A prime cap b prime cap c prime is 5 times smaller than triangle cap A cap b cap c and is 5 times as far from the center point of dilation. - no response given%0D%0A%0D%0ATriangle A′B′C′%0D%0A%0D%0A′%0D%0A%0D%0A′%0D%0A%0D%0A′%0D%0A is 5 times as large as triangle ABC%0D%0A%0D%0A%0D%0A%0D%0A and is 5 times as far from the center point of dilation.%0D%0ATriangle cap A prime cap b prime cap c prime is 5 times as large as triangle cap A cap b cap c and is 5 times as far from the center point of dilation. - not selected, this is the correct answer%0D%0A%0D%0ATriangle A′B′C′%0D%0A%0D%0A′%0D%0A%0D%0A′%0D%0A%0D%0A′%0D%0A is 5 times smaller than triangle ABC%0D%0A%0D%0A%0D%0A%0D%0A and is 5 times closer to the center point of dilation.%0D%0A Triangle cap A prime cap b prime cap c prime is 5 times smaller than triangle cap A cap b cap c and is 5 times closer to the center point of dilation. - incorrect%0D%0AScore
Triangle A′B′C′ is 5 times larger than triangle ABC and is 5 times as far from the center point of dilation.
explain how
When a shape undergoes a dilation, it is either enlarged or reduced in size. The scale factor determines the degree of enlargement or reduction. In this case, the scale factor is 5, which means that every side length of triangle ABC is multiplied by 5 to get the corresponding side length of triangle A′B′C′.
Since the center point of dilation is at the origin (0, 0), the dilation occurs outward from this point. The farther a point on the shape is from the center, the greater its distance will be from the center after the dilation. So, triangle A′B′C′ is 5 times as far from the origin as triangle ABC.
Combining these two factors, we can conclude that triangle A′B′C′ is 5 times larger than triangle ABC and is 5 times as far from the center of dilation.