Question

The figure shows two similar triangles on a coordinate grid:

Which set of transformations have been performed on triangle ABC to form triangle A'B'C'?

A.)Dilation by a scale factor of 2 followed by reflection about the X-axis
B.)Dilation by a scale factor of 4 followed by reflection about the x-axis
C.)Dilation by a scale factor of 2 followed by reflection about the y-axis
D.)Dilation by a scale factor of 4 followed by reflection about the y-axis

Answer 1

C. Dilation by a scale factor of 2 followed by reflection about the y-axis

Explanation:

You are given triangle with vertices A(1,2), B(0,0) and C(3,-1).

1. Dilation by a factor of 2 has the rule:

(x,y)→(2x,2y)

So,

• A(1,2)→A''(2,4);
• B(0,0)→B''(0,0);
• C(3,-1)→C''(6,-2).

2. Reflection about the y-axis has the rule:

(x,y)→(-x,y)

So,

• A''(4,2)→A'(-4,2);
• B''(0,0)→B'(0,0);
• C''(6,-2)→C'(-6,-2).

Points A', B' and C' are exactly vertices of the triangle A'B'C' shown in the diagram.