Question

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′ . 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.

Answer 1

To find the coordinates of ΔA'B'C', we first apply the first transformation rule to the original coordinates of ΔABC:

A: (x+4, y-6) = (-8+4, 4-6) = (-4, -2)
B: (x+4, y-6) = (-5+4, 8-6) = (-1, 2)
C: (x+4, y-6) = (-3+4, 3-6) = (1, -3)

Now, we apply the second transformation rule to the coordinates of ΔA'B'C':

A': (x+5, y-3) = (-4+5, -2-3) = (1, -5)
B': (x+5, y-3) = (-1+5, 2-3) = (4, -1)
C': (x+5, y-3) = (1+5, -3-3) = (6, -6)

Therefore, ΔA'B'C' has the following coordinates: A' (1, -5), B' (4, -1), and C' (6, -6).

To find the rule for the composition transformation, we simply combine the two transformation rules:

Composition rule: (x,y) → (x+4+5, y-6-3) = (x+9, y-9)

The image of ΔABC after the composition transformation will be in the fourth quadrant.