Question

Use the image to answer the question.

A coordinate plane's axes range from 0 to 5, both by 1-unit increments. Solid triangle upper A upper B upper C and dotted triangle upper A prime upper B prime upper C prime are plotted.

Image Long DescriptionTriangle upper A prime upper B prime upper C prime is enclosed within triangle upper A upper B upper C. Triangle upper A upper B upper C has vertices located as follows: upper A at the origin, upper B at left parenthesis 2 comma 4 right parenthesis, and upper C at left parenthesis 4 comma 2 right parenthesis. Triangle upper A prime upper B prime upper C prime has vertices located as follows: upper A prime at the origin, upper B prime at left parenthesis 1 comma 2 right parenthesis, and upper C prime at left parenthesis 2 comma 1 right parenthesis.

Do the dilations of AB¯¯¯¯¯¯¯¯
, BC¯¯¯¯¯¯¯¯
, and AC¯¯¯¯¯¯¯¯
pass through the center of dilation if the center of dilation is the origin?

(1 point)
Responses

A′B′¯¯¯¯¯¯¯¯¯¯
, B′C′¯¯¯¯¯¯¯¯¯¯¯
, and A′C′¯¯¯¯¯¯¯¯¯¯¯
all pass through the center of dilation because ΔABC
is an enlargement of ΔA′B′C′
by a scale factor of 2 and the center of dilation is at (1.5, 1.5)
.
line segment cap A prime cap b prime , line segment cap b prime cap c prime , and line segment cap A prime cap c prime all pass through the center of dilation because triangle upper A upper B upper C is an enlargement of triangle upper A prime upper B prime upper C prime by a scale factor of 2 and the center of dilation is at open paren 1 point 5 comma space 1 point 5 close paren .

A′B′¯¯¯¯¯¯¯¯¯¯
and A′C′¯¯¯¯¯¯¯¯¯¯¯
do not pass through the center of dilation because they are on the same line as AB¯¯¯¯¯¯¯¯
and AC¯¯¯¯¯¯¯¯
in the preimage, and B′C′¯¯¯¯¯¯¯¯¯¯¯
does pass through the center of dilation because it is taken to a parallel line.
line segment cap A prime cap b prime and line segment cap A prime cap c prime do not pass through the center of dilation because they are on the same line as line segment cap A cap b and line segment cap A cap c in the preimage, and line segment cap b prime cap c prime does pass through the center of dilation because it is taken to a parallel line.

A′B′¯¯¯¯¯¯¯¯¯¯
, B′C′¯¯¯¯¯¯¯¯¯¯¯
, and A′C′¯¯¯¯¯¯¯¯¯¯¯
do not pass through the center of dilation because ΔABC
is an enlargement of ΔA′B′C′
by a scale factor of 2 and the center of dilation is at (1.5, 1.5)
.
line segment cap A prime cap b prime , line segment cap b prime cap c prime , and line segment cap A prime cap c prime do not pass through the center of dilation because triangle upper A upper B upper C is an enlargement of triangle upper A prime upper B prime upper C prime by a scale factor of 2 and the center of dilation is at open paren 1 point 5 comma space 1 point 5 close paren .

A′B′¯¯¯¯¯¯¯¯¯¯
and A′C′¯¯¯¯¯¯¯¯¯¯¯
pass through the center of dilation because they are on the same line as AB¯¯¯¯¯¯¯¯
and AC¯¯¯¯¯¯¯¯
in the preimage, and B′C′¯¯¯¯¯¯¯¯¯¯¯
does not pass through the center of dilation because it is taken to a parallel line.
line segment cap A prime cap b prime and line segment cap A prime cap c prime pass through the center of dilation because they are on the same line as line segment cap A cap b and line segment cap A cap c in the preimage, and line segment cap b prime cap c prime does not pass through the center of dilation because it is taken to a parallel line.
Remaining Attempts : 3
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is it a, b, c, or, d. You moke

Answer 1

D.

A and A' are at the origin, so AB and AC (and their images A'B' and A'C') lie on rays through the center and thus pass through it. BC and its image B'C' are parallel to each other and do not pass through the origin.