Angle ABC contains the points A (-5,3), B(-4,-2), and C (1,4). Describe the effect of the dilation of the angle with a scale factor of 8 and a center of dilation at the origin (0,0).
A dilation with a scale factor of 8 and a center of dilation at the origin (0,0) will stretch all points in the angle away from the origin by a factor of 8.
Let's find the coordinates of the image points:
Image of A = (-5×8, 3×8) = (-40, 24)
Image of B = (-4×8, -2×8) = (-32, -16)
Image of C = (1×8, 4×8) = (8, 32)
Therefore, the image of angle ABC, denoted as angle A'B'C', has the points A' (-40, 24), B' (-32, -16), and C' (8, 32).
To describe the effect of the dilation of the angle ABC with a scale factor of 8 and a center of dilation at the origin (0,0), we need to determine the coordinates of the dilated points.
First, let's find the coordinates of the dilated points A', B', and C' using the formula for dilation:
For a point (x, y) dilated with a scale factor of k and a center of dilation at (h, j):
The coordinates of the dilated point (x', y') are given by:
x' = h + k(x - h)
y' = j + k(y - j)
Now let's find the coordinates of the dilated points:
For point A (-5, 3):
x' = 0 + 8(-5 - 0) = -40
y' = 0 + 8(3 - 0) = 24
So the coordinates of A' are (-40, 24).
For point B (-4, -2):
x' = 0 + 8(-4 - 0) = -32
y' = 0 + 8(-2 - 0) = -16
So the coordinates of B' are (-32, -16).
For point C (1, 4):
x' = 0 + 8(1 - 0) = 8
y' = 0 + 8(4 - 0) = 32
So the coordinates of C' are (8, 32).
The effect of the dilation with a scale factor of 8 and a center of dilation at the origin (0,0) is that the angle ABC is enlarged by a factor of 8. The angle becomes larger and its vertices move farther away from the origin. The lengths of the sides of the angle are multiplied by 8, and the angle itself remains the same.