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.

1 answer

To find the coordinates of ΔA'B'C', we need to apply the given transformations one by one.

1. Transformation (x,y)→(x+4,y−6):
For point A(-8,4):
New x-coordinate = -8 + 4 = -4
New y-coordinate = 4 - 6 = -2
So, A'(-4, -2)

For point B(-5,8):
New x-coordinate = -5 + 4 = -1
New y-coordinate = 8 - 6 = 2
So, B'(-1, 2)

For point C(-3,3):
New x-coordinate = -3 + 4 = 1
New y-coordinate = 3 - 6 = -3
So, C'(1, -3)

2. Transformation (x,y)→(x+5,y−3):
For point A'(-4, -2):
New x-coordinate = -4 + 5 = 1
New y-coordinate = -2 - 3 = -5
So, A''(1, -5)

For point B'(-1, 2):
New x-coordinate = -1 + 5 = 4
New y-coordinate = 2 - 3 = -1
So, B''(4, -1)

For point C'(1, -3):
New x-coordinate = 1 + 5 = 6
New y-coordinate = -3 - 3 = -6
So, C''(6, -6)

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

Since all the x-coordinates are positive and all the y-coordinates are negative, ΔA''B''C'' will be in the fourth quadrant after the transformations.