dilations practice
Sure, here are some practice problems for dilations:
1) Determine the coordinates of the dilated point (4, 2) by a scale factor of 2 with a center of dilation at the origin.
Solution: The coordinates of the dilated point can be found by multiplying each coordinate by the scale factor. Therefore, the dilated point would be (8, 4).
2) A triangle has vertices A(2, 3), B(4, 1), and C(6, 5). Determine the coordinates of the dilated triangle when scaled down by a scale factor of 0.5 with a center of dilation at the origin.
Solution: To find the dilated coordinates of each vertex, multiply each coordinate by the scale factor. The dilated triangle would have vertices A'(1, 1.5), B'(2, 0.5), and C'(3, 2.5).
3) Given a rectangle with vertices A(3, 2), B(3, -2), C(-3, -2), and D(-3, 2), dilate the rectangle by a scale factor of 3 with a center of dilation at the origin.
Solution: Multiply each coordinate of the rectangle by the scale factor to find the dilated coordinates. The dilated rectangle would have vertices A'(9, 6), B'(9, -6), C'(-9, -6), and D'(-9, 6).
4) A line segment has endpoints A(2, 3) and B(6, 3). Dilate the line segment by a scale factor of 0.75 with a center of dilation at the origin.
Solution: To dilate a line segment, multiply the coordinates of each endpoint by the scale factor. The dilated line segment would have endpoints A'(1.5, 2.25) and B'(4.5, 2.25).
5) A shape has vertices A(1, 2), B(2, 4), C(3, 2), and D(2, 0). Dilate the shape by a scale factor of 2 with a center of dilation at (1, 1).
Solution: Subtract the coordinates of the center of dilation from each vertex, dilate the resulting coordinates by the scale factor, then add the coordinates of the center of dilation back to find the dilated vertices. The dilated shape would have vertices A'(1, 3), B'(2, 5), C'(3, 3), and D'(2, 1).
Remember to practice dilations using different scale factors and centers of dilation to further enhance your understanding and skills.