The rigid motion that produces the image ΔABC ΔDEF are a reflection across the x-axis and a translation two units to the right
C. T(2, 0) ○
The steps used to find the rigid motion that produces are as follows;
The rigid transformation that produces the image DEF from the pre-image ABC include a reflection across the x-axis and translation two units to the right
The coordinates of the vertices of the triangle ABC are A(-3, -2), B(-4, -4), and C(-3, -4). The coordinates of the vertices image of the triangle ABC following a reflection across the x-axis are; A’(-3, 2), B’(-4, 4), and C’(-3, 4)
The coordinates of the image of the triangle A’B’C’ following a translation 2 units to the right are;
A’’(-3 + 2, 2) = A’’(-1, 2)
B’’(-4 + 2, 4) = B’’(-2, 4)
C’’(-3 + 2, 4) = C’’(-1, 4)
The coordinates of the triangle DEF are; D(-1, 2), E(-2, 4), and F(-1, 4), therefore, the triangle ABD is mapped to the triangle DEF by a reflection across the x-axis and a translation two units to the right, which corresponds to Option C