Question

Write the coordinates of the vertices after a dilation with a scale factor of 1/5, centered at the origin.

Answer 1

The coordinates of the vertices after the dilation by a scale factor 1/5 centered at the origin will be:

• U'(-1, -2)

• V'(0, -2)

• W'(-1, 2)

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:

• U'(-1, -2)

• V'(0, -2)

• W'(-1, 2)