Question

Graph the image of this figure after a dilation with a scale factor of 2 centered at (2, 2) .

Answer 1

Answer:

The points of the dilated figure would be at (-2, 10), (2, 6), and (-8, 4); an image of the figure is attached.

Step-by-step explanation:

First we translate the center of dilation and figure so the origin becomes the center of dilation.

Since the point (2, 2) is our center of dilation, we must translate it left 2 and down 2 to make the origin the center; this means we map every point

(x, y)→(x-2, y-2)

The scale factor of 2 means that each point will be multiplied by 2; this gives us the rule

(x, y)→(2x-4, 2y-4)

Lastly we will translate the figure right 2 and up 2 to move it back to its original position; this gives us the rule

(x,y)→(2x-4+2, 2y-4+2) = (2x-2, 2y-2)

The first point in the original figure, at the top, is (0, 6).  Applying the transformation gives us

(0, 6)→(2*0-2, 2*6-2) = (0-2, 12-2) = (-2, 10)

The point on the right of the pre-image is (2, 4).  Applying the transformation rule gives us

(2, 4)→(2*2-2, 2*4-2) = (4-2, 8-2) = (2, 6)

The point on the left of the pre-image is at (-3, 3).  Applying the transformation rule, we have

(-3, 3)→(-3*2-2, 3*2-2) = (-6-2, 6-2) = (-8, 4)

Answer 2

The dilated figure would end up at -2,-2