Graph the image of the given triangle after the transformation that has the rule (x, y)→(−x, −y).

Question

Select the Polygon tool. Then, click the points of the triangle vertices to create the triangle by connecting the sides. You may use the "Move" tool to move your vertices or completed triangle as needed.

The original triagnle:

A.(6,7)
B. (7,4)
C. (-2,5)

Answer 1

To graph the image of the triangle after the transformation represented by the rule \((x, y) \rightarrow (-x, -y)\), we will first apply the transformation to each vertex of the triangle.

1. Original Vertices:

   • A: \((6, 7)\)
   • B: \((7, 4)\)
   • C: \((-2, 5)\)

2. Applying the Transformation:

   • For point A: \[ A' = (-6, -7) \]
   • For point B: \[ B' = (-7, -4) \]
   • For point C: \[ C' = (2, -5) \]

3. Transformed Vertices:

   • A': \((-6, -7)\)
   • B': \((-7, -4)\)
   • C': \((2, -5)\)

Now, to graph the original triangle and its transformed image:

1. Plot the original vertices A, B, and C on the coordinate plane.
2. Connect the points A, B, and C to form the original triangle.
3. Plot the transformed vertices A', B', and C' on the coordinate plane.
4. Connect the points A', B', and C' to form the transformed triangle.

After you have plotted and connected the points, the graph should show the original triangle and the transformed triangle reflecting across the origin.