Questions: Reflect triangle ABC over the x-axis. Translate DEFG 4 units right and 5 units down.

Solution Steps

To reflect a point (x, y) over the x-axis, the x-coordinate remains the same, and the y-coordinate changes its sign. The vertices of triangle ABC are A(6,4), B(8,1), and C(6,1).

A'(6, -4) B'(8, -1) C'(6, -1)

To translate a point (x, y) 4 units right and 5 units down, we add 4 to the x-coordinate and subtract 5 from the y-coordinate. The vertices of DEFG are D(-6, 7), E(-4, 7), F(-4, 2), and G(-6, 2).

D'(-6 + 4, 7 - 5) = D'(-2, 2) E'(-4 + 4, 7 - 5) = E'(0, 2) F'(-4 + 4, 2 - 5) = F'(0, -3) G'(-6 + 4, 2 - 5) = G'(-2, -3)

Final Answer