Question

A sequence of transformations maps ABC A(-6,4) B(-2, 6) C (-4,2) to A’B’C’ A’(12,-2) B’(16,2) C’(12,0). The sequence of transformations that maps ABC to ABC is a reflection across the _________ followed by translation ______.

a) x-axis, 18 units to the right
b) y-axis, 18 units up
c) y-axis, 18 units down
d) x-axis, 18 units to the left

Answer 1

The sequence of transformations that maps triangle ABC to A'B'C' is a reflection across the x-axis followed by translation of 18 units to the right.

Step-by-step explanation:

To determine the sequence of transformations that maps triangle ABC to triangle A'B'C', we first need to analyze the coordinates given for the original and transformed triangles.

Point A maps to A', changing from A(-6,4) to A'(12,-2). This change involves two steps:

Reflecting across an axis

Translating the points

Inspecting the y-values, we see that the original positive y-values become negative in the transformed triangle, which implies a reflection across the x-axis. Next, we notice that the x-values increased by 18 units, from -6 to 12 for point A, which is a horizontal movement. This translation is 18 units to the right side of the coordinate system.

Therefore, the sequence of transformations is a reflection across the x-axis followed by a translation of 18 units to the right. The correct answer is:

a) x-axis, 18 units to the right