Questions: Triangle DEF is reflected over the y-axis, and then translated down 4 units and right 3 units. Which congruency statement describes the figures? Triangle DEF ≈ Triangle SUR Triangle DEF ≈ Triangle SRU Triangle DEF ≈ Triangle RUS

Solution Steps

When reflecting a point over the y-axis, the x-coordinate changes its sign, and the y-coordinate remains the same.

• D(5, 5) becomes D'(-5, 5)
• E(5, 8) becomes E'(-5, 8)
• F(2, 2) becomes F'(-2, 2)

When translating a point down 4 units, subtract 4 from the y-coordinate. When translating a point right 3 units, add 3 to the x-coordinate.

• D'(-5, 5) becomes D''(-2, 1)
• E'(-5, 8) becomes E''(-2, 4)
• F'(-2, 2) becomes F''(1, -2)

The transformed triangle D''E''F'' has vertices D''(-2, 1), E''(-2, 4), and F''(1, -2). Comparing these to the vertices of triangle SRU, we have:

• S(-4, 2)
• R(-4, 5)
• U(-1, -2) Notice that if we translate triangle SRU 3 units to the right and down 1 unit, then
• S(-4,2) becomes S'(−1,1)
• R(-4,5) becomes R'(−1,4)
• U(-1,-2) remains U(−1,-2)

Similarly, if we translate DEF 1 unit up and 3 units left,

• D(5, 5) becomes D'(2,6)
• E(5, 8) becomes E'(2,9)
• F(2, 2) becomes F'(-1,3)

The transformed vertices D''E''F'' match the vertices of triangle SRU after a reflection and translation. Specifically, D corresponds to S, E corresponds to R, and F corresponds to U.

Final Answer: ∆DEF ≅ ∆SRU