Question
Determine the skill factor using the dilation of line, segment AB, with a centerpoint of dilation at the origin.
A = (9, 9)
B = (6, 6)
AB after:
A = (3, 3)
B= (2, 2)
A = (9, 9)
B = (6, 6)
AB after:
A = (3, 3)
B= (2, 2)
Answers
GPT 3.5
The dilation factor can be calculated by taking the ratio of the lengths of the original line segment to the dilated line segment.
The length of line segment AB before dilation can be found using the distance formula:
AB = sqrt[(9-6)^2 + (9-6)^2]
AB = sqrt[3^2 + 3^2]
AB = sqrt(18)
AB = 3sqrt(2)
The length of line segment AB after dilation can be found in the same way:
AB = sqrt[(3-2)^2 + (3-2)^2]
AB = sqrt[1^2 + 1^2]
AB = sqrt(2)
Therefore, the dilation factor is:
3sqrt(2) / sqrt(2) = 3
So, the skill factor using the dilation is 3.
The length of line segment AB before dilation can be found using the distance formula:
AB = sqrt[(9-6)^2 + (9-6)^2]
AB = sqrt[3^2 + 3^2]
AB = sqrt(18)
AB = 3sqrt(2)
The length of line segment AB after dilation can be found in the same way:
AB = sqrt[(3-2)^2 + (3-2)^2]
AB = sqrt[1^2 + 1^2]
AB = sqrt(2)
Therefore, the dilation factor is:
3sqrt(2) / sqrt(2) = 3
So, the skill factor using the dilation is 3.