Question

Which transformation correctly justifies the congruence of △ ABC and △ DEF based on their coordinates?

a) △ ABC is stretched vertically by a factor of 2, then reflected across the x-axis.
b) △ ABC is dilated by a factor of 2, then reflected across the y-axis.
c) △ ABC is reflected across the x-axis, then translated to the right.
d) △ ABC is reflected across the y-axis, then stretched horizontally by a factor of 2.

Answer 1

The correct transformation that justifies the congruence of △ ABC and △ DEF based on their coordinates is option d) △ ABC is reflected across the y-axis, then stretched horizontally by a factor of 2.

Step-by-step explanation:

The correct transformation that justifies the congruence of △ ABC and △ DEF based on their coordinates is option d) △ ABC is reflected across the y-axis, then stretched horizontally by a factor of 2.

To justify the congruence of two triangles based on their coordinates, we need to apply the appropriate transformations to one triangle to obtain the coordinates of the other triangle. Since option d reflects the triangle across the y-axis first and then stretches it horizontally by a factor of 2, it preserves the shape and size of the triangle, making it congruent to the other triangle.