Question

determine the scale factor used in the dilation of line segment A(4,-12) and B (8,-16), centered at the origin.
a) 1/4
b) 4
c) -4
d) 2

Answer 1

wrong. try again

Answer 2

To calculate the scale factor used in the dilation, we can divide the length of the dilated line segment by the length of the original line segment.

The length of the original line segment AB is:
AB = sqrt((8-4)^2 + (-16-(-12))^2)
= sqrt((4)^2 + (-4)^2)
= sqrt(16 + 16)
= sqrt(32)
= 4sqrt(2)

The length of the dilated line segment A'B' can be found in the same way:
A'B' = sqrt((2*4)^2 + (2*(-16))^2)
= sqrt((8)^2 + (-32)^2)
= sqrt(64 + 1024)
= sqrt(1088)
= 8sqrt(34)

The scale factor can be found by dividing the length of the dilated line segment A'B' by the length of the original line segment AB:

Scale factor = A'B' / AB
= (8sqrt(34)) / (4sqrt(2))
= 2sqrt(34) / sqrt(2)
= 2sqrt(34/2)
= 2sqrt(17)

Therefore, the scale factor used in the dilation is not one of the options provided (a, b, c, or d).

Answer 3

Apologies for the mistake. Let's try again.

The length of the original line segment AB is:
AB = sqrt((8-4)^2 + (-16-(-12))^2)
= sqrt((4)^2 + (-4)^2)
= sqrt(16 + 16)
= sqrt(32)
= 4sqrt(2)

The length of the dilated line segment A'B' can be found in the same way:
A'B' = sqrt((2*4)^2 + (2*(-16))^2)
= sqrt((8)^2 + (-32)^2)
= sqrt(64 + 1024)
= sqrt(1088)
= 8sqrt(17)

The scale factor can be found by dividing the length of the dilated line segment A'B' by the length of the original line segment AB:

Scale factor = A'B' / AB
= (8sqrt(17)) / (4sqrt(2))
= 2sqrt(17) / sqrt(2)
= 2sqrt(17/2)
= 2sqrt(8.5)

The scale factor is approximately 2sqrt(8.5). However, none of the provided options (a, b, c, or d) match this value exactly.