Answer:
These new coordinates represent the vertices of the dilated triangle after a scale factor of 1/4 around the origin:
P'(0, -1)
Q'(2, 0)
R'(0, 1)
Explanation:
let's dilate the triangle with vertices P(0, -4), Q(8, 0), and R(0, 4) around the origin with a scale factor of 1/4. Here are the steps:
Identify the original coordinates:
P(0, -4)
Q(8, 0)
R(0, 4)
Apply the dilation formula:
For each vertex, we'll multiply both the x and y coordinates by 1/4.
Calculate the new coordinates:
For vertex P(0, -4):
x' = (1/4) * 0 = 0
y' = (1/4) * (-4) = -1
So, the new coordinates for P' are (0, -1).
For vertex Q(8, 0):
x' = (1/4) * 8 = 2
y' = (1/4) * 0 = 0
So, the new coordinates for Q' are (2, 0).
For vertex R(0, 4):
x' = (1/4) * 0 = 0
y' = (1/4) * 4 = 1
So, the new coordinates for R' are (0, 1).
These new coordinates represent the vertices of the dilated triangle after a scale factor of 1/4 around the origin:
P'(0, -1)
Q'(2, 0)
R'(0, 1)