Question
Determine the scale factor used in the dilation of line segment A and B centered at the origin A'(2,3) B'(4,1) A'(6,9) B'(12,3)
Answers
GPT 3.5
To determine the scale factor used in the dilation of line segment A and B, we can calculate the ratio of the lengths of the original line segment and the dilated line segment.
The original line segment AB has endpoints A(2,3) and B(4,1). Its length can be calculated using the distance formula:
Length of AB = sqrt((4-2)^2 + (1-3)^2) = sqrt(4 + 4) = sqrt(8)
The dilated line segment A'B' has endpoints A'(6,9) and B'(12,3). Its length can also be calculated using the distance formula:
Length of A'B' = sqrt((12-6)^2 + (3-9)^2) = sqrt(36 + 36) = sqrt(72)
The scale factor is the ratio of the lengths of the dilated line segment to the original line segment:
Scale factor = Length of A'B' / Length of AB
= sqrt(72) / sqrt(8)
= sqrt(9)*sqrt(8) / sqrt(8)
= 3
Therefore, the scale factor used in the dilation of line segment A and B is 3.
The original line segment AB has endpoints A(2,3) and B(4,1). Its length can be calculated using the distance formula:
Length of AB = sqrt((4-2)^2 + (1-3)^2) = sqrt(4 + 4) = sqrt(8)
The dilated line segment A'B' has endpoints A'(6,9) and B'(12,3). Its length can also be calculated using the distance formula:
Length of A'B' = sqrt((12-6)^2 + (3-9)^2) = sqrt(36 + 36) = sqrt(72)
The scale factor is the ratio of the lengths of the dilated line segment to the original line segment:
Scale factor = Length of A'B' / Length of AB
= sqrt(72) / sqrt(8)
= sqrt(9)*sqrt(8) / sqrt(8)
= 3
Therefore, the scale factor used in the dilation of line segment A and B is 3.