Question

Triangle ABC has vertices at A(0, 5), B(4,4), and C(-1,0). Graph the image ofTriangle A'B'C' for the translation (x, y) = (x - 2, V - 1). Graph the preimageTriangle ABC, the image. Triangle A'B'C', and identify the coordinates of A, B, and C.​

Answer 1

To find the image of triangle A'B'C' after the translation (x, y) = (x - 2, y - 1), we subtract 2 from the x-coordinate and 1 from the y-coordinate of each vertex of triangle ABC. The new coordinates are A'(-2, 4), B'(2, 3), and C'(-3, -1). This translation shifts the triangle 2 units left and 1 unit down.

Step-by-step explanation:

The question involves performing a translation on a triangle in the coordinate plane. We are given the original coordinates of triangle ABC and need to apply the translation (x, y) = (x - 2, y - 1) to obtain the coordinates for triangle A'B'C'. The original vertices of triangle ABC are given by A(0, 5), B(4, 4), and C(-1, 0). Applying the translation, we get the following new coordinates:

• A'(0 - 2, 5 - 1) = A'(-2, 4)
• B'(4 - 2, 4 - 1) = B'(2, 3)
• C'(-1 - 2, 0 - 1) = C'(-3, -1)

After plotting both triangles on a coordinate plane, we can see the image of triangle A'B'C' has been shifted 2 units to the left and 1 unit down from the preimage triangle ABC.