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

Option C is right.

Step-by-step 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

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