Triangle PQR has vertives P(2, -4), Q(4, -5), and R(7, -2). It is translated 6 units left and 3 units up to produce Triangle P'Q'R'. Complete table.

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06-09-2022
Mathematics

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Triangle PQR has vertives P(2, -4), Q(4, -5), and R(7, -2). It is translated 6 units left and 3 units up to produce Triangle P'Q'R'. Complete table.

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xero099 xero099 · Answer 1 · 2022-09-16T18:57:44+02:00

The coordinates of the triangle P'Q'R' is P'(x, y) = (- 4, - 1), Q'(x, y) = (- 2, - 2) and R'(x, y) = (1, 1), respectively.

What are the locations of the vertices of the triangle after applying rigid transformations?

In this problem we know the three vertices of a triangle on a Cartesian plane and we must determine the coordinates of its image by applying rigid transformations. According to the statement, the vertices of the image are obtained by applying a translation formula:

P'(x, y) = P(x, y) + T(x, y) (1)

Where:

P(x, y) - Original point
P'(x, y) - Resulting point
T(x, y) - Translation vector

If we know that P(x, y) = (2, - 4), Q(x, y) = (4, - 5), R(x, y) = (7, - 2) and T(x, y) = (- 6, 3), then the coordinates of the vertices of the image are:

P'(x, y) = (2, - 4) + (- 6, 3)

P'(x, y) = (- 4, - 1)

Q'(x, y) = (4, - 5) + (- 6, 3)

Q'(x, y) = (- 2, - 2)

R'(x, y) = (7, - 2) + (- 6, 3)

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

The coordinates of the triangle P'Q'R' is P'(x, y) = (- 4, - 1), Q'(x, y) = (- 2, - 2) and R'(x, y) = (1, 1), respectively.

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

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