Answer: (-2,-4), (2,1) and (7,-5)
Explanation:
When rotating a point 180 degrees about the origin a point A(x,y) becomes A'(-x,-y).
When translating a point B(x,y) by 'h' units left, then the new point will become B'(x-h,y).
Given: A triangle with coordinates (6,4), (2, -1), and (-3,5) is translated 4 units left and rotated 180° about the origin.
Translation rule for 4 units left : (x,y) → (x-h,y)
The new coordinates will be (6-4,4) , (2-4,-1) and (-3-4, 5)
i.e. (2,4), (-2,-1) and (-7,5) .
Now, applying the rotation rule of 180 degrees we get the points of the final image as
(-2,-4), (2,1) and (7,-5) .
Hence, the coordinates of its image is (-2,-4), (2,1) and (7,-5) .