Can anyone graph this please!!!
5. Perform these transformations on ∆TRL and compute the perimeter of the pre-image and final image.
a. Rotate ∆TRL 180° about the origin and label the resulting image ∆T’ R’ L’.
b. Reflect ∆T’ R’ L’ across the y-axis and label the resulting image ∆T’’ R’’ L’’.
c. Translate ∆T’’ R’’ L’’ according to (x, y) →(x + 3, y – 3) and label the image ∆T’’’ R’’’ L’’’.
To graph these transformations, you need to start with the original triangle ∆TRL and apply each transformation step by step. Here's how you can do it:
1. Start by graphing the original triangle ∆TRL. Choose any three points to represent the vertices of the triangle. For example, you could choose T(0,0), R(3,0), and L(1,2). Plot these points on a coordinate plane.
2. Rotate ∆TRL 180° about the origin: To rotate the triangle, you can use the following rotation formula for each vertex:
- To rotate point T(x, y) 180° about the origin, the new coordinates will be T'(-x, -y).
- To rotate point R(x, y) 180° about the origin, the new coordinates will be R'(-x, -y).
- To rotate point L(x, y) 180° about the origin, the new coordinates will be L'(-x, -y).
Apply this formula to each vertex of ∆TRL to find the new coordinates of ∆T'R'L'. Plot these new points on the graph.
3. Reflect ∆T'R'L' across the y-axis: To reflect the triangle across the y-axis, you simply need to change the sign of the x-coordinates of each vertex. The new coordinates will be:
- Point T''(x, y) becomes T''(-x, y).
- Point R''(x, y) becomes R''(-x, y).
- Point L''(x, y) becomes L''(-x, y).
Apply this transformation to each vertex of ∆T'R'L' and plot the new points on the graph.
4. Translate ∆T''R''L'' according to (x, y) →(x + 3, y – 3): To translate the triangle, you need to add 3 to the x-coordinate and subtract 3 from the y-coordinate for each vertex. The new coordinates will be:
- Point T'''(x, y) becomes T'''(x + 3, y - 3).
- Point R'''(x, y) becomes R'''(x + 3, y - 3).
- Point L'''(x, y) becomes L'''(x + 3, y - 3).
Apply this transformation to each vertex of ∆T''R''L'' and plot the final points on the graph.
Now that you have the final image ∆T'''R'''L''', you can calculate the perimeter of both the pre-image (∆TRL) and the final image (∆T'''R'''L'''). To compute the perimeter, you need to find the length of each side of the triangle and then add them up.
Remember to measure the distances between the vertices of the triangle on the graph to find the side lengths. Once you have found the side lengths, add them up to calculate the perimeter of both ∆TRL and ∆T'''R'''L'''.
I hope this helps you graph the transformations and compute the perimeters of the pre-image and final image!