Triangle abc has vertices a (0,0) b (5,-1) and c (3,7) . what are the vertices of the resulting image when the triangle is translated 4 units to the left then dilated by a scale factor of 2?

When the vertices of the triangle are translated 4 units to the left, you only have to subtract 4 to the x-coordinate:
A'(-4,0)
B'(1,-1)
C'(-1,7)

Dilating the triangle to a scale factor of 2, we simply multiply the coordinates by 2. This means that the triangle is enlarged.
A'(-8,0)
B'(2,-2)
C'(-2,14)