Question

Select the correct answer from each drop-down menu. The graph shows a triangle plotted on a coordinate plane. The triangle is at A (0, 0), B (1, 3), and C (1, 1). ∆ABC is translated 2 units down and 1 unit to the left. Then it is rotated 90° clockwise about the origin to form ∆A′B′C′.

The coordinates of vertex A′ of ∆A′B′C′ are (-1, -2).
The coordinates of vertex B′ of ∆A′B′C′ are (-4, -1).
The coordinates of vertex C′ of ∆A′B′C′ are (-2, 1).

Answer 1

To find the coordinates of the vertices of triangle A′B′C′ after translation and rotation, we need to apply the given translations and rotation to the coordinates of triangle ABC.

Step-by-step explanation:

To find the coordinates of the vertices of triangle A′B′C′ after translation and rotation, we need to apply the given translations and rotation to the coordinates of triangle ABC.

First, we translate the triangle 2 units down and 1 unit to the left. This means subtracting 2 from the y-coordinates and 1 from the x-coordinates of all three points.

Next, we rotate the translated triangle 90° clockwise about the origin. To do this, we swap the x and y coordinates of each point and negate the new x-coordinate. The resulting coordinates are A′(-1, -2), B′(-4, -1), and C′(-2, 1).