Question

Use the function rules to find the coordinates of ΔA"B"C"
Δ
A
"
B
"
C
"
and predict the quadrant it will be in after the transformations. ΔABC
Δ
A
B
C
, with coordinates A(−8,4)
A
(
−
8
,
4
)
, B(−5,8)
B
(
−
5
,
8
)
, and C(−3,3)
C
(
−
3
,
3
)
, is transformed by (x,y)→(x+4,y−6)
(
x
,
y
)
→
(
x
+
4
,
y
−
6
)
to produce ΔA′B′C′
Δ
A
′
B
′
C
′
. ΔA′B′C′
Δ
A
′
B
′
C
′
is transformed by the rule (x,y)→(x+5,y−3)
(
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 in 4 easy worded sentences

Answer 1

First, we apply the transformation (x, y) → (x + 4, y - 6) to the original coordinates of ΔABC. This results in A'(-4, -2), B'(-1, 2), and C'(2, -3). Next, we apply the second transformation (x, y) → (x + 5, y - 3) to these new coordinates, yielding A" (1, -5), B" (4, -1), and C" (7, -6). Since all these coordinates have a positive x-value and a negative y-value, ΔA"B"C" will be located in the fourth quadrant.