Question

translate the triangle whose vertices are (1,5), (4,7), and (7,0), 8 units to the left and then rotate it 90 degrees clockwise about the origin.

Answer 1

The final triangle has vertices (5, 7), (7, 4) and (0, 1)

Step-by-step explanation:

To translate the triangle 8 units to the left, we use the following rule

(x, y) ----> (x - 8, y)

Then, the vertices of the triangle after the translation is

(1, 5) ----> (1 - 8, 5) = (-7, 5)

(4, 7) ----> (4 - 8, 7) = (-4, 7)

(7, 0) -----> (7 - 8, 0) = (-1, 0)

Now, we need to rotate the figure 90 degrees clockwise about the origin, so we will use the rule

(x, y) ----> (y, -x)

Then, the vertices of the triangle are

(-7, 5) ----> (5, -(-7)) = (5, 7)

(-4, 7) ----> (7, -(-4)) = (7, 4)

(-1, 0) ----> (0, -(-1)) = (0, 1)

Therefore, the final triangle has vertices (5, 7), (7, 4) and (0, 1)