HELP Graph the image of the figure after a dilation with a scale factor of 1/4 centered at (5, −5).

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.

x = 10.1

step-by-step explanation:

all of the angles of a tirangle add up to 180º

180 - 65 = 115 (since we already know the value of one angle)

(2x + 7) + (8x + 7) = 115

(combins like terms) 10x + 14 = 115

(isolate the variable subtract 14 from both sides): 10x = 101

(find the variable divide both sides by 10): x = 101/10

x = 10.1

answer:

step-by-step explanation: