Question

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

A Coordinate grid (plane, graph, whichever one you like to use) with two triangles on it. Triangle ABC and Triangle A'B'C'. Chart below tells you where the points are placed:

ABC / A= (-12, 12) / B= (-9, 6) / C= (-3, 12)
A'B'C' / A'= (4, -4) / B'= (3, -2) / C'= (1, -4)

Which statement is correct for ▲ABC and ▲A'B'C'?
1. ▲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.
2. ▲ABC ~ ▲A'B'C' , because ▲A'B'C' is obtained by dilating ▲ABC by a scale factor of 1/4 and then rotating it about the origin by 90 degrees.
3. ▲ABC ~ ▲A'B'C' , because ▲A'B'C' is obtained by dilating ▲ABC by a scale factor of 1/4 and then rotating it about the origin by 180 degrees.
4. ▲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.

Answer 1

1. ▲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.

Explanation:

given;

ABC / A= (-12, 12) / B= (-9, 6) / C= (-3, 12)

A'B'C' / A'= (4, -4) / B'= (3, -2) / C'= (1, -4)

consider line AC = 9

A'C' = 3

ratio is 9/3, so the factor is 1/3