Question

Consider rst in the coordinate plane.


Which dilation of rst would result in a line segment with a slope of 2 that passes 4,2 through?

A.
a dilation with a scale factor of 6 centered at
B.
a dilation with a scale factor of 2 centered at
C.
a dilation with a scale factor of 0.5 centered at
D.
a dilation with a scale factor of 4 centered
Consider in the coordinate plane.


Which dilation of would result in a line segment with a slope of 2 that passes through ?

A.
a dilation with a scale factor of 6 centered at
B.
a dilation with a scale factor of 2 centered at
C.
a dilation with a scale factor of 0.5 centered at
D.
a dilation with a scale factor of 4 centered at

Answer 1

The location of the point (4, 2) is to the right of the triangle RST, therefore,

a dilation from the left or a contraction from the right is required.

The dilation of ΔRST that would result in a line segment with slope of 2

that passes through (4, 2) is C. A dilation with a scale factor of 0.5 centered

at $\underline{(12, \, 2)}$

Reasons:

The given vertex of the line are;

R(-2, 6), T(-6, -2), S(6, -4)

$The \ slope \ of \ the \ line \ \overline{RT} = \dfrac{6 - (-2)}{-2 - (-6)} = 2$

Point on the lint RT that has the same y-coordinate as the point (4, 2) is (-4, 2)

Taking the center of dilation as the point (12, 2), we have;

Coordinates of the point (-4, 2) relative to the point (12, 2) is found as

follows;

(-4 - 12, 2 - 2) = (-16, 0)

Therefore, dilating (-16, 0) by $\overline {RT}$ a scale factor of 0.5, with a center at (12,

2) gives;0.5 × (-16, 0) = (-8, 0)

The actual location of the point (-8, 0) is (-8 + 12, 0 + 2 ) = (4, 2)

Therefore, the dilation of ΔRST that would result in a line segment with

slope of 2 that passes through (4, 2) is C. A dilation with a scale factor of 0.5 centered at $\underline{(12, \, 2)}$

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