Use the function rules to find the coordinates of ΔA"B"C"

Question

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.(4 points)

Answer 1

To find the coordinates of ΔA'B'C', we can apply the transformation rules step by step.

Applying the first transformation rule (x,y)→(x+4,y−6) to ΔABC:
A' = (-8+4, 4-6) = (-4, -2)
B' = (-5+4, 8-6) = (-1, 2)
C' = (-3+4, 3-6) = (1, -3)

Now, applying the second transformation rule (x,y)→(x+5,y−3) to ΔA'B'C':
A" = (-4+5, -2-3) = (1, -5)
B" = (-1+5, 2-3) = (4, -1)
C" = (1+5, -3-3) = (6, -6)

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

To predict the quadrant that ΔA"B"C" will be in, we can look at the signs of the x and y coordinates.
Since the x coordinates are positive and the y coordinates are negative, ΔA"B"C" will be in the fourth quadrant.