The coordinates of the vertices after a dilation with a scale factor of 3, centered at the origin are R'(-9, -6), S'(-9, 3), T'(9, 3), and U'(9, -6).
What is the scale factor?
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 of 3 centered at the origin.
Given the vertices of the rectangle;
R(-3, -2)= R'(-3 × 3, -2× 3) = R'(-9, -6)
S(-3, 1) = S'(-3 × 3, 1× 3) = S'(-9, 3)
T(3, 1) = T'('3 × 3, 1 × 3) = T'(9, 3)
U (3, -2)= R'(3 × 3, -2× 3) = U'(9, -6)
Hence, the coordinates of the vertices after a dilation with a scale factor of 3, centered at the origin are R'(-9, -6), S'(-9, 3), T'(9, 3), and U'(9, -6).
Learn more about scale factors here;
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