Question
What would the scale factor used in the dilation of the line segment be if AB Was (1, 3) and (2, -4) then (4, -12) and (8, -16)?
Answers
GPT 3.5
The scale factor used in the dilation of the line segment can be found by comparing the lengths of the line segments before and after dilation.
The length of line segment AB can be calculated using the distance formula:
AB = √[(2-1)^2 + (-4-3)^2]
AB = √[1^2 + 7^2]
AB = √(1 + 49)
AB = √50
AB ≈ 7.07
The length of line segment CD can be calculated using the distance formula:
CD = √[(8-4)^2 + (-16-(-12))^2]
CD = √[4^2 + (-4)^2]
CD = √(16 + 16)
CD = √32
CD ≈ 5.66
The scale factor can be calculated by dividing the length of the dilated segment by the length of the original segment:
Scale factor = CD / AB
Scale factor = 5.66 / 7.07
Scale factor ≈ 0.8
Therefore, the scale factor used in the dilation of the line segment is 0.8.
The length of line segment AB can be calculated using the distance formula:
AB = √[(2-1)^2 + (-4-3)^2]
AB = √[1^2 + 7^2]
AB = √(1 + 49)
AB = √50
AB ≈ 7.07
The length of line segment CD can be calculated using the distance formula:
CD = √[(8-4)^2 + (-16-(-12))^2]
CD = √[4^2 + (-4)^2]
CD = √(16 + 16)
CD = √32
CD ≈ 5.66
The scale factor can be calculated by dividing the length of the dilated segment by the length of the original segment:
Scale factor = CD / AB
Scale factor = 5.66 / 7.07
Scale factor ≈ 0.8
Therefore, the scale factor used in the dilation of the line segment is 0.8.