Question

Triangle ABC is transformed to obtain triangle A′B′C′:

(Attachment Below)

Which statement is correct for ABC and A′B′C′?
A. ABC - A′B′C′ because A′B′C′ is obtained by dilating ABC by a scale factor of 1/6 and then rotating it about the origin by 90 degrees
B. ABC - A′B′C′ because A′B′C′ is obtained by dilating ABC by a scale factor of 1/2 and then rotating it about the origin by 180 degrees
C. ABC - A′B′C′ because A′B′C′ is obtained by dilating ABC by a scale factor of 1/3 and then rotating it about the origin by 180 degrees
D. ABC - A′B′C′ because A′B′C′ is obtained by dilating ABC by a scale factor of 1/3 and then rotating it about the origin by 90 degrees

Answer 1

Option C is right.

Explanation:

Given is a graph with two triangles marked on it.

Triangle ABC is in the I quadrant with vertices (2,2) (2,10) and (8,12)

Triange A'B'C' is in the III quadrant with vertices (-1,-1), (-1,-5) and (-4,-6)

On comparison we find corresponding side of AB is A'B'

Length of AB = 8 and Length of A'B' = 4.

Hence A'B'C' is obtained by dilating ABC by a scale factor of 1/2.

Now since moved to III quadrant from I quadrant we find that there is a rotation of triangle ABC about the origin. The degree of rotation is 180 degrees.

Hence A'B'C' is obtained by dilating ABC by a scale factor of 1/2 and then rotating it about the origin by 180 degrees