Question

Triangle abc is rotated 90 degrees clockwise around the origin to form triangle a'b'c'. Then triangle a'b'c' is dilated using a scale factor of 3/2 with a center of dilation at vertex a' to form triangle a"b"c". What is the relationship between triangle abc and triangle a"b"c"?

1) Triangle abc is similar to triangle a''b''c''
2) Triangle abc is congruent to triangle a''b''c''
3) Triangle abc is a reflection of triangle a''b''c''
4) Triangle abc is an enlargement of triangle a''b''c''

Answer 1

After a rotation and a dilation transformation, triangle abc is similar to triangle a"b"c", with sides of the latter being 3/2 times longer.

Step-by-step explanation:

The relationship between triangle abc and triangle a"b"c" can be determined by examining the effects of the transformations applied. First, triangle abc is rotated 90 degrees clockwise around the origin to form triangle a'b'c'. A rotation does not change the size or shape of a geometric figure, so triangles abc and a'b'c' are congruent. Then triangle a'b'c' is dilated using a scale factor of 3/2 with a center of dilation at vertex a' to form triangle a"b"c". The dilation changes the size but not the shape, meaning that triangle a"b"c" is similar to triangle abc, with corresponding sides that are 3/2 times as long. Thus, option 1 is correct: Triangle abc is similar to triangle a"b"c".