use the function rules describe the coordinates of angle ABC and predict a quadrant. It will be an after the transformation angle ABC with coordinates a -8,4 B -5,8 and C -3,3 is transform formed by XY equals X plus 4Y -6 to produce angle A’B’C’. A’B’C’ is transformed by XY equals X plus 5Y -3 create the rule for the composition transformation in predict what quadrant the image will be in
To find the coordinates of angle ABC, we are given the points A(-8,4), B(-5,8), and C(-3,3).
To predict the quadrant of angle ABC, we can look at the signs of the x and y coordinates of point A. Since the x-coordinate is negative (-8) and the y-coordinate is positive (4), angle ABC is located in the second quadrant.
The next step is to apply the given transformation XY = X + 4Y - 6 to angle ABC to produce angle A'B'C'.
To find the coordinates of A'B'C', we will substitute the coordinates of A, B, and C into the transformation rule:
For point A(-8,4):
X = -8
Y = 4
We plug in the values:
XY = X + 4Y - 6
(-8)(4) = (-8) + 4(4) - 6
-32 = -8 + 16 - 6
-32 = 2
Therefore, the transformed coordinates for point A' are (2,4).
Similarly, for point B(-5,8):
X = -5
Y = 8
We plug in the values:
XY = X + 4Y - 6
(-5)(8) = (-5) + 4(8) - 6
-40 = -5 + 32 - 6
-40 = 21
Therefore, the transformed coordinates for point B' are (21,8).
Lastly, for point C(-3,3):
X = -3
Y = 3
We plug in the values:
XY = X + 4Y - 6
(-3)(3) = (-3) + 4(3) - 6
-9 = -3 + 12 - 6
-9 = 3
Therefore, the transformed coordinates for point C' are (3,3).
Now, to find the composition transformation, we need to apply the second transformation XY = X + 5Y - 3 to the coordinates A'B'C'.
For point A' (2,4):
X = 2
Y = 4
We plug in the values:
XY = X + 5Y - 3
(2)(4) = (2) + 5(4) - 3
8 = 2 + 20 - 3
8 = 19
Therefore, the transformed coordinates for point A" are (8,4).
For point B' (21,8):
X = 21
Y = 8
We plug in the values:
XY = X + 5Y - 3
(21)(8) = (21) + 5(8) - 3
168 = 21 + 40 - 3
168 = 58
Therefore, the transformed coordinates for point B" are (168,8).
For point C' (3,3):
X = 3
Y = 3
We plug in the values:
XY = X + 5Y - 3
(3)(3) = (3) + 5(3) - 3
9 = 3 + 15 - 3
9 = 15
Therefore, the transformed coordinates for point C" are (9,3).
From the transformed coordinates, we can see that the image point A", B", and C" are all located in the first quadrant.
Hence, the image angle A'B'C' will be located in the first quadrant.