Question

Which dilation of △ RST would result in a line segment with a slope of 2 that passes through ( − 4 , 2 ) ?

Answer 1

A dilation of ∆ RST by a factor of 2 would result in a line segment with a slope of 2 passing through (-4, 2).

What is dilation factor?

For a dilation of a triangle, the ratio of corresponding side lengths determines the dilation factor.

We want the resulting line segment to have a slope of 2 and pass through the point (-4, 2),

we use the point-slope form y - y₁ = m(x - x₁)

The equation with a slope of 2 passing through(-4, 2)is:

y - 2 = 2(x + 4)

y = 2x + 10

find the corresponding dilation factor by comparing this with the original line segment's equation. The dilation factor for the sides of the triangle would be the coefficient of 2 in the equation above.

Thus, the dilation factor is 2, and a dilation of ∆ RST by a factor of 2 would result in a line segment with a slope of 2 passing through (-4, 2).

Answer 2

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 12,2

Explanation: