A triangle with coordinates (6,4), (2, -1), and (-3,5) is translated 4 units left and rotated 180° about the origin. What are the coordinates of its image?
A. (2,4),(-2,-1), (-7,5)
B. (4,6),(-1,2), (5, -3)
C. (4,-2),(-1,2), (5,7)
D. (4,2), (-1,-2), (5, -7)

The book has these as the optional answers but I keep getting (-2,-4), (2,1), (7, -5)
Can someone help me??

(-2,-4), (2,1) and (7,-5)

Step-by-step 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) .

step-by-step explanation:

a'(12.5,11.25)

slope=(y1-y2)/(x1-x2)