Trapezoid RSTV with vertices R(-1,1), S(4, 1), T(4, -1), and V(-1, -3) and is reflected across y = -3

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03-09-2022
Mathematics

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Trapezoid RSTV with vertices R(-1,1), S(4, 1), T(4, -1), and V(-1, -3) and is reflected across y = -3

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xero099 xero099 · Answer 1 · 2022-09-09T21:41:51+02:00

The vertices of the image are R'(x, y) = (- 1, - 7), S'(x, y) = (4, - 7), T'(x, y) = (4, - 5) and V'(x, y) = (- 1, - 3).

What are the coordinates of the vertices of the image by using a reflection formula?

In this question we know the locations of the four vertices of the trapezoid RSTV and we need to determine the coordinates of its image by using a reflection formula about an axis parallel to the y-axis, whose formula is described below:

P'(x, y) = P(x, y) - 2 · [P(x, y) - (p, k)]

Where:

p - x-Coordinate of the original point.
k - y-Coordinate of the reflection axis.
P(x, y) - Original point
P'(x, y) - Resulting point

Now we proceed to find the coordinates of the images:

R'(x, y) = (- 1, 1) - 2 · [(- 1, 1) - (- 1, - 3)]

R'(x, y) = (- 1, 1) - 2 · (0, 4)

R'(x, y) = (- 1, 1) + (0, - 8)

R'(x, y) = (- 1, - 7)

S'(x, y) = (4, 1) - 2 · [(4, 1) - (4, - 3)]

S'(x, y) = (4, 1) - 2 · (0, 4)

S'(x, y) = (4, 1) + (0, - 8)

S'(x, y) = (4, - 7)

T'(x, y) = (4, - 1) - 2 · [(4, - 1) - (4, - 3)]

T'(x, y) = (4, - 1) - 2 · (0, 2)

T'(x, y) = (4, - 1) + (0, - 4)

T'(x, y) = (4, - 5)

V'(x, y) = (- 1, - 3) - 2 · [(- 1, - 3) - (- 1, - 3)]

V'(x, y) = (- 1, - 3) - 2 · (0, 0)

V'(x, y) = (- 1, - 3)

The vertices of the image are R'(x, y) = (- 1, - 7), S'(x, y) = (4, - 7), T'(x, y) = (4, - 5) and V'(x, y) = (- 1, - 3).

To learn more on rigid transformations: https://brainly.com/question/1761538

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