1. **State the problem:** We have triangle \(\triangle A'B'C'\) with points \(A'(-5,-6)\), \(B'(-6,-2)\), and \(C'(-3,-3)\). We apply a glide reflection \(T_{(3,0)} \circ R_m\), where \(R_m\) is reflection about the line \(y=-4\), followed by translation \(T_{(3,0)}\). 2. **Reflect points about line \(y=-4\):** The reflection of a point \((x,y)\) about \(y=-4\) is \((x, -8 - y)\) because the distance from \(y\) to \(-4\) is \(d = y + 4\), and the reflected point is \(y' = -4 - d = -8 - y\). Calculate each reflected point: - \(A'(-5,-6) \to A_r(-5, -8 - (-6)) = (-5, -8 + 6) = (-5, -2)\) - \(B'(-6,-2) \to B_r(-6, -8 - (-2)) = (-6, -8 + 2) = (-6, -6)\) - \(C'(-3,-3) \to C_r(-3, -8 - (-3)) = (-3, -8 + 3) = (-3, -5)\) 3. **Apply translation \(T_{(3,0)}\):** Add 3 to the x-coordinate of each reflected point: - \(A'' = (-5 + 3, -2 + 0) = (-2, -2)\) - \(B'' = (-6 + 3, -6 + 0) = (-3, -6)\) - \(C'' = (-3 + 3, -5 + 0) = (0, -5)\) 4. **Final coordinates of \(\triangle A''B''C''\):** \(A''(-2, -2), B''(-3, -6), C''(0, -5)\) 5. **Compare with options:** None of the options exactly match these coordinates, but option C is closest in pattern. Let's verify option C: - Option C: \(A''(-2, -5), B''(0, -2), C''(-3, -1)\) which does not match our results. Since none of the options match the exact computed points, re-check the reflection formula: Reflection about \(y = k\) for point \((x,y)\) is \((x, 2k - y)\). Here, \(k = -4\), so reflection is \((x, -8 - y)\) as used. Recalculate reflected points: - \(A'(-5,-6) \to (-5, 2(-4) - (-6)) = (-5, -8 + 6) = (-5, -2)\) - \(B'(-6,-2) \to (-6, -8 + 2) = (-6, -6)\) - \(C'(-3,-3) \to (-3, -8 + 3) = (-3, -5)\) Translation by \((3,0)\): - \(A'' = (-5 + 3, -2) = (-2, -2)\) - \(B'' = (-6 + 3, -6) = (-3, -6)\) - \(C'' = (-3 + 3, -5) = (0, -5)\) No option matches exactly, but option C is the closest if points are permuted. Possibly a typo in options. **Answer:** Coordinates after glide reflection are \(A''(-2, -2), B''(-3, -6), C''(0, -5)\). None of the given options match exactly.