Question

Graph the image of this figure after a dilation with a scale factor of 1/2 centered at the point (−3, 0) . Use the polygon tool to graph the dilated figure.

Answer 1

Answer:

The graph is attached.

Step-by-step explanation:

First we find the slope of the line that would pass through the point of dilation, (-3, 0), and each vertex.

From (-3, 0) to (5, 4), the slope would be

m = (4-0)/(5--3) = 4/8

Since the scale factor is 1/2, this means each part of the slope would be multiplied by this scale factor:

(4(1/2))/(8(1/2)) = 2/4

This means from our point of dilation we count up 2 and over 4; this puts the new point at (-3+4, 0+2) = (1, 2).

From (-3, 0) to (3, 8) the slope is

m = (8-0)/(3--3) = 8/6

Multiplying the rise and run by 1/2, we have

(8(1/2))/(6(1/2)) = 4/3

This means the dilated point would be up 4 and over 3 from (-3, 0), putting it at (-3+3, 0+4) = (0, 4).

From (-3, 0) to (-5, 4), the slope is

m = (4-0)/(-5--3) = 4/-2.

Multiplying the rise and run by 1/2, we have

(4(1/2))/(-2(1/2)) = 2/-1

This means the dilated point would be up 2 and over -1 from (-3, 0), putting it at (-3+-1, 0+2) = (-4, 2).

These three vertices give us the dilated figure.