Question

Which transformation or sequence of transformations maps △abc to △a'b'c' ? two triangles, a b c, and a b c prime are drawn on a coordinate grid with vertices plotted as follows: a at (5, 5), b at (1, 3), c at (2, 1), a prime at (0, negative 5), b prime at (negative 4, negative 3), and c prime at (negative 3, negative 1).

a. a translation 5 units left
b. a reflection across x=0, then a translation 5 units left
c. a reflection across y=0, then a translation 5 units left
d. a rotation 90° about the origin

Answer 1

The transformation that maps △abc to △a'b'c' is a reflection across the y-axis (x=0) followed by a translation 5 units left, corresponding to Option B.

Step-by-step explanation:

To determine which transformation or sequence of transformations maps △abc to △a'b'c', we need to analyze the coordinates of the triangles' vertices. Originally, we have vertices at A(5, 5), B(1, 3), and C(2, 1). The transformed vertices are A'(0, -5), B'(-4, -3), and C'(-3, -1). Analyzing these points, we can observe that each x-coordinate of the original triangle has been multiplied by -1 and moved 5 units to the left, and each y-coordinate also has been multiplied by -1. The transformation that affects the x and y coordinates in such a manner is a reflection across the y-axis followed by a translation 5 units left.

Therefore, the correct option that describes the sequence of transformations is a reflection across the y-axis (which is the same as x=0), followed by a translation 5 units left. Option B - a reflection across x=0, then a translation 5 units left - would be the correct sequence of transformations for mapping △abc to △a'b'c'.