Subjects geometry

Triangle Reflections Ec7Cd8

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1. The problem is to graph triangle $\triangle FGH$ and its image reflected across the lines $x = -1$ and $y = 1$. 2. Reflection across a vertical line $x = a$ changes a point $(x,y)$ to $(2a - x, y)$. 3. Reflection across a horizontal line $y = b$ changes a point $(x,y)$ to $(x, 2b - y)$. 4. We first identify the coordinates of points $F$, $G$, and $H$ from the left graph (not provided explicitly, so we assume coordinates for demonstration). 5. Apply reflection across $x = -1$ to each vertex to get the first image. 6. Apply reflection across $y = 1$ to each vertex to get the second image. 7. Plot the original triangle and its two images accordingly. Since exact coordinates are not given, the SVG will show the original triangle and its reflections across the lines $x=-1$ and $y=1$ with labels.
F G H F' G' H' F'' G'' H'' x = -1 y = 1