Question

Use the image to answer the question.

A coordinate plane's x-axis ranges from negative 3 to 16 and its y-axis ranges from negative 3 to 10, both by 1-unit increments. Points upper D and upper F are plotted and connected by a dotted line that extends past both points.

Find point H
to prove that DH¯¯¯¯¯¯¯¯¯
is an enlargement of DF¯¯¯¯¯¯¯¯
by a scale factor of 2 with point D
as the center of dilation.

(1 point)
Responses

H
is at (13,6)
.
upper H is at left parenthesis 13 comma 6 right parenthesis .

H
is at (5.5,3)
.
upper H is at left parenthesis 5.5 comma 3 right parenthesis .

H
is at (−2,0)
.
upper H is at left parenthesis negative 2 comma 0 right parenthesis .

H
is at (8,18)
.
upper H is at left parenthesis 8 comma 18 right parenthesis .

Answer 1

H is at (13, 6).

Reason: For a dilation with center D and scale factor 2, H = D + 2( F − D ) = 2F − D. Using the coordinates of D and F from the graph gives H = (13, 6).