You rotate a triangle 90° counterclockwise about the origin. then you translate its image 1 unit left and 2 units down. the vertices of the final image are (-5,,2) and (-2,-1) . what are the vertices of the original triangle?

The coordinates of the original triangle are (2,4). (4,1) and (1,1)

Step-by-step explanation:

About the origin, I have to rotate a triangle 90° counterclockwise. Then I translate its image 1 unit left and 2 units down.

The vertices of the final image are (-5,0), (-2,2), and (-2,-1).

We need to get the vertices of the original triangle.

So, start from a triangle with vertices (-5,0), (-2,2), and (-2,-1) and do the reverse to get the original triangle.

So, we will translate the image triangle by 1 unit right and 2 units up and we will get the triangle with vertices (-5 + 1, 0 + 2), (- 2 + 1, 2 + 2) and (- 2 +1, - 1 + 2)  ≡ (-4,2), (-1, 4) and (-1,1).

Now, we have to rotate this intermediate triangle by 90° clockwise.

Therefore, the coordinates of the original triangle are (2,4). (4,1) and (1,1) (Answer)

{Since, for 90° rotation the coordinates of all the vertices will interchange their location (i.e. x-value to y-value and y-value to x-value) and a negative sign will be added to the y-coordinate of the interchanged coordinates}