Determine the scale factor used in the dilation of line segment AB, centered at the origin.

Question

A (6, 9) B (12, 3)
A (2, 3) B (4, 1)

Answer 1

To find the scale factor, we can compare the lengths of the original line segment AB and the image line segment AB'.

The length of AB is determined by the distance formula:

AB = √[(x2 - x1)^2 + (y2 - y1)^2]
= √[(12 - 6)^2 + (3 - 9)^2]
= √[6^2 + (-6)^2]
= √[36 + 36]
= √72
= 6√2

Next, we calculate the length of AB':

AB' = √[(x2 - x1)^2 + (y2 - y1)^2]
= √[(4 - 2)^2 + (1 - 3)^2]
= √[2^2 + (-2)^2]
= √[4 + 4]
= √8
= 2√2

To find the scale factor, we divide the length of AB' by the length of AB:

Scale factor = AB' / AB
= (2√2) / (6√2)
= (2/6)
= 1/3

Therefore, the scale factor used in the dilation of line segment AB, centered at the origin, is 1/3.

Answer 2

wrong

Answer 3

Sorry about that mistake.

To find the scale factor, we can compare the lengths of the original line segment AB and the image line segment AB'.

The length of AB is determined by the distance formula:

AB = √[(x2 - x1)^2 + (y2 - y1)^2]
= √[(12 - 6)^2 + (3 - 9)^2]
= √[6^2 + (-6)^2]
= √[36 + 36]
= √72
= 6√2

Next, we calculate the length of AB':

AB' = √[(x2 - x1)^2 + (y2 - y1)^2]
= √[(4 - 2)^2 + (1 - 3)^2]
= √[2^2 + (-2)^2]
= √[4 + 4]
= √8
= 2√2

To find the scale factor, we divide the length of AB' by the length of AB:

Scale factor = AB' / AB
= (2√2) / (6√2)
= 2/6
= 1/3

Therefore, the scale factor used in the dilation of line segment AB, centered at the origin, is 1/3.