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 the transformations mentioned, we need the coordinates of the vertices of triangle TRL. Without the specific coordinates, we won't be able to perform the transformations accurately. Could you please provide the coordinates of vertices T, R, and L?
To graph the transformations of the triangle ∆TRL, follow these steps:
Step 1: Draw the original triangle ∆TRL.
Start by drawing a triangle on a coordinate plane. Label the vertices T, R, and L. You can choose any arbitrary coordinates for each vertex, for example, T(0,0), R(2,0), and L(0,3).
Step 2: Rotate ∆TRL 180° about the origin to create ∆T'R'L'.
To rotate the triangle, you need to apply the following rule: (x', y') = (-x, -y) for each vertex (x, y) of the original triangle. Apply this rule to each vertex of ∆TRL to find the new vertices of ∆T'R'L'. For example, the coordinates of T' will be (-0, -0) = (0, 0).
Step 3: Reflect ∆T'R'L' across the y-axis to create ∆T''R''L''.
To reflect the triangle across the y-axis, you need to apply the following rule: (x'', y'') = (-x', y') for each vertex (x', y') of the rotated triangle. Apply this rule to each vertex of ∆T'R'L' to find the new vertices of ∆T''R''L''. For example, the coordinates of T'' will be (-0, 0) = (0, 0).
Step 4: Translate ∆T''R''L'' according to (x, y) →(x + 3, y – 3) to create ∆T'''R'''L'''.
To translate the triangle, you need to add the given values (3, -3) to the coordinates of each vertex of ∆T''R''L''. Apply this rule to each vertex to find the new vertices of ∆T'''R'''L'''. For example, the coordinates of T''' will be (0 + 3, 0 - 3) = (3, -3).
Step 5: Compute the perimeter of the pre-image and final image.
To compute the perimeter of the pre-image ∆TRL, measure the lengths of each side using the distance formula and add them together. For example, the perimeter can be calculated as the sum of the lengths of TR, RL, and LT.
To compute the perimeter of the final image ∆T'''R'''L''', measure the lengths of each side using the distance formula and add them together. For example, the perimeter can be calculated as the sum of the lengths of T'''R''', R'''L''', and L'''T'''.
Following these steps, you can graph the transformations of the triangle ∆TRL and compute the perimeters of the pre-image and final image.