Question

reflections, and rotations
date 11/20 block 2
graph the image of the figure using the transformation given.

1. translation: ((x, y) \to (x - 8, y + 4))
2. translation: ((x, y) \to (x - 5, y + 3))
3. reflection across the x - axis
4. reflection across the y - axis
5. rotation (90^circ) counterclockwise about the origin
6. rotation (180^circ) about the origin

Explanation:

Step1: Identify Original Points (Take Problem 1 as Example)

For triangle \(MLN\) in Problem 1, find coordinates: Let's assume grid has 1 unit per square. Suppose \(M\) is \((4,1)\), \(L\) is \((4,2)\), \(N\) is \((3, -1)\) (visually from graph).

Step2: Apply Translation \((x,y)\to(x - 8,y + 4)\)

• For \(M(4,1)\): \(x'=4 - 8=-4\), \(y'=1 + 4 = 5\) → \(M'(-4,5)\)
• For \(L(4,2)\): \(x'=4 - 8=-4\), \(y'=2 + 4 = 6\) → \(L'(-4,6)\)
• For \(N(3,-1)\): \(x'=3 - 8=-5\), \(y'=-1 + 4 = 3\) → \(N'(-5,3)\)

Step3: Plot Translated Points

Plot \(M'\), \(L'\), \(N'\) on grid and connect to get translated triangle.

(Repeat similar steps for other problems: For reflection over x - axis, use \((x,y)\to(x,-y)\); over y - axis, \((x,y)\to(-x,y)\); 90° counterclockwise: \((x,y)\to(-y,x)\); 180°: \((x,y)\to(-x,-y)\), then plot new points.)

Answer:

(For each problem, the graph is drawn by applying the transformation to each vertex of the original figure and connecting the new vertices. Since it's a graphing task, the final answer is the visual graph obtained by the above steps for each sub - problem. For example, in Problem 1, the translated triangle has vertices at \((-4,5)\), \((-4,6)\), \((-5,3)\) plotted and connected.)