Answer:
The figure is dilated by a scale factor of 1/2 and then translated
A(-6, 8) → A''(3, 2)
The algebraic description that will complete the transformation is:
(x, y) → (x/2 + 6, y/2 - 2)
Explanations:
Let us first consider the coordinates of A, B, and C.
A(-6, 8)
B(-4, 10)
C(-2, 6)
Let us also consider the coordinates of A'', B'', and C''
A''(3, 2)
B''(4, 3)
C''(5, 1)
To know the scale factor for dilation:
A''B'' / AB = 1 / 2 = 0.5
The scale factor for dilation = 2
The coordinates for the vertices, A', B', and C' are therefore:
A'(0.5x-6, 8x0.5) = A' (-3, 4)
B'(0.5x-4, 10x0.5) = B'(-2, 5)
C'(0.5x-2, 6x0.5) = C'(-1, 3)
The triangle A'B'C' was then translated by 6 in the horizontal direction and -2 in the vertical direction.
A''(-3+6, 4-2) = A''(3, 2)
B''(-2+6, 5-2) = B''(4, 3)
C''(-1+6, 3-2) = C''(5, 1)
The figure is dilated by a scale factor of 1/2 and then translated
A(-6, 8) → A''(3, 2)
The algebraic description that will complete the transformation is:
(x, y) → (x/2 + 6, y/2 - 2)