Use the function rules to find the coordinates of ΔA”B”C”and predict the quadrant it will be in after the transformations. ΔABC, with coordinates A(−8,4) B(−5,8), and C(−3,3), is transformed by (x,y)→(x+4,y−6) to produce ΔA’B’C’ is transformed by the rule (x,y)→(x+5,y−3). Create the rule for the composition transformation and predict what quadrant the image will be in.(4 points)

Answer 1

To find the coordinates of ΔA"B"C", we need to apply the transformation rules to each of the vertices of ΔABC.

For point A:
(x, y) → (x + 4, y - 6)
(-8, 4) → (-8 + 4, 4 - 6) → (-4, -2)

For point B:
(x, y) → (x + 4, y - 6)
(-5, 8) → (-5 + 4, 8 - 6) → (-1, 2)

For point C:
(x, y) → (x + 4, y - 6)
(-3, 3) → (-3 + 4, 3 - 6) → (1, -3)

The coordinates of ΔA"B"C" are A"(-4, -2), B"(-1, 2), and C"(1, -3).

Next, we need to apply the transformation rule (x, y) → (x + 5, y - 3) to ΔA"B"C".

For point A":
(x, y) → (x + 5, y - 3)
(-4, -2) → (-4 + 5, -2 - 3) → (1, -5)

For point B":
(x, y) → (x + 5, y - 3)
(-1, 2) → (-1 + 5, 2 - 3) → (4, -1)

For point C":
(x, y) → (x + 5, y - 3)
(1, -3) → (1 + 5, -3 - 3) → (6, -6)

The coordinates of ΔA"B"C" are A"(1, -5), B"(4, -1), and C"(6, -6).

From the coordinates of the transformed triangle, we can predict the quadrant it will be in. Since all three vertices have positive x-values and negative y-values, ΔA"B"C" will likely be in Quadrant IV. However, please note that the exact quadrant also depends on the scale of the graph and the position of the original triangle.