Answer:
The coordinates of the vertices after the dilation by a scale factor 1/5 centered at the origin will be:
Step-by-step explanation:
We know that when an object is dilated by a scale factor, it gets reduced, stretched, or remains the same, depending upon the value of the scale factor.
If the scale factor > 1, the image is enlarged
If the scale factor is between 0 and 1, it gets shrunk
If the scale factor = 1, the object and the image are congruent
Rule to calculate the dilation by a scale factor 1/5 centered at the origin
P(x, y) → P'(1/5x, 1/5y)
Here, P'(1/5, 1/5y) is the image of P(x, y).
Given the vertices of the triangle UVW
U (-5, -10)
V (0, -10)
W (-5, 10)
so
Rule to calculate the dilation by a scale factor 1/5 centered at the origin
P(x, y) → P'(1/5x, 1/5y)
U (-5, -10) → U'(1/5(-5), 1/5(-10)) → U'(-1, -2)
V (0, -10) → V'(1/5(0), 1/5(-10)) → V'(0, -2)
W (-5, 10) → W'(1/5(-5), 1/5(10)) → W'(-1, 2)
Therefore, the coordinates of the vertices after the dilation by a scale factor 1/5 centered at the origin will be:
