Answer:
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)(x,y)→(
4
1
(x−5)+5,
4
1
(y+5)−5)
or
(x, y) \rightarrow (\frac{1}{4}x+\frac{15}{4}, \frac{1}{4}y-\frac{15}{4} )(x,y)→(
4
1
x+
4
15
,
4
1
y−
4
15
)
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)→A
′
(
4
1
(−3)+
4
15
,
4
1
(7)−
4
15
)
A(-3, 7) \rightarrow A'(3, -2)A(−3,7)→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)→B
′
(
4
1
(−7)+
4
15
,
4
1
(−5)−
4
15
)
B(-7, -5) \rightarrow B'(2, -5)B(−7,−5)→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)→C
′
(
4
1
(9)+
4
15
,
4
1
(3)−
4
15
)
C(9, 3) \rightarrow C'(6, -3)C(9,3)→C
′
(6,−3)
As, you can see the graph as shown below in the attachment.