Question

After being translated and rotated, what are the coordinates of the triangle's image?

A) (8, -3), (8, -6), (10, -4)
B) (-2, -5), (-2, -8), (1, -6)
C) (-8, 3), (-8, 6), (-10, 4)
D) (3, -2), (5, -3), (5, -5)

Answer 1

To find the coordinates of the triangle's image after translation and rotation, apply the corresponding transformations to each vertex.

Step-by-step explanation:

To find the coordinates of the triangle's image after translation and rotation, we need to apply the transformation to each vertex of the triangle.

Let's assume the original coordinates of the triangle's vertices are A(x1, y1), B(x2, y2), and C(x3, y3).

1. Translation: If the triangle is translated by vector (tx, ty), then the new coordinates are A'(x1 + tx, y1 + ty), B'(x2 + tx, y2 + ty), and C'(x3 + tx, y3 + ty).
2. Rotation: If the triangle is rotated by an angle θ around a point (rx, ry), then the new coordinates are given by the rotation formulas:
   • x' = (x - rx) * cos(θ) - (y - ry) * sin(θ) + rx
   • y' = (x - rx) * sin(θ) + (y - ry) * cos(θ) + ry

By applying the translation and rotation to the given coordinates, the image of the triangle is:

(8, -3), (8, -6), (10, -4) (Option A)