Question

A triangle is translated ( (x+2, y-10)) and then rotated 90 degrees. If the triangle starts at A(-4,-2), B(3,4), C(-5,6) ), where does the triangle end it's journey?

Answer 1

The coordinates of the triangle after translation and rotation are A''(12,-2), B''(6,-5), C''(4,-3).

Step-by-step explanation:

To translate the triangle by (x+2, y-10), we add 2 to the x coordinate and subtract 10 from the y coordinate of each vertex. So, the new coordinates of A, B, and C would be (-4+2, -2-10), (3+2, 4-10), and (-5+2, 6-10) respectively. Therefore, the new coordinates of the triangle after translation would be A'(-2,-12), B'(5,-6), C'(-3,-4).

To rotate the triangle 90 degrees, we use the rotation matrix. Multiplying the new coordinates of each vertex by this matrix will give us the final position of the triangle. The rotation matrix for a 90 degree counterclockwise rotation is [0 -1; 1 0]. Multiplying this matrix with the coordinates of each vertex, we get the new coordinates of the triangle after rotation as A''(12,-2), B''(6,-5), C''(4,-3).