Question

Graph the image of the figure after a dilation with a scale factor of 14 centered at (5, −5) .

Answer 1

Check the attached file for the answer. Correction in the problem it is 1/4 not 14.

Answer 2

Given:

Scale factor(k) = 1/4,  and centered at (5, -5).

Labelled the given figure as A, B and C.

The coordinates of the given triangle ABC are;

A = (-3, 7)

B = (-7, -5)

C = (9, 3)

To find the image of the figure after a dilation with scale factor 1/4 centered at (5, -5).

The rule of dilation with scale factor 1/4 and centered at (5, -5) is given by;

$(x, y) \rightarrow (\frac{1}{4}(x-5)+5, \frac{1}{4}(y+5)-5)$

or

$(x, y) \rightarrow (\frac{1}{4}x+\frac{15}{4}, \frac{1}{4}y-\frac{15}{4} )$

The coordinates of the image of the figure after dilation are;

$A(-3, 7) \rightarrow A'(\frac{1}{4}(-3)+\frac{15}{4}, \frac{1}{4}(7)-\frac{15}{4} )$

$A(-3, 7) \rightarrow A'(3, -2)$

$B(-7, -5) \rightarrow B'(\frac{1}{4}(-7)+\frac{15}{4}, \frac{1}{4}(-5)-\frac{15}{4} )$

$B(-7, -5) \rightarrow B'(2, -5)$

and

$C(9, 3) \rightarrow C'(\frac{1}{4}(9)+\frac{15}{4}, \frac{1}{4}(3)-\frac{15}{4} )$

$C(9, 3) \rightarrow C'(6, -3)$

As, you can see the graph as shown below in the attachment.