Question

HELP ASAP!! Identify the matrix transformation of ΔPQR, which has coordinates P(−5, −2),Q(−6, −3), and R(−2, −3), for reflection across the y-axis. Then identify the correct vertices of the image.

Answer 1

P'= (5,-2), Q'= (6,-3), R'= (2,-3)

Explanation:

Answer 2

Matrix transformation =
`\left[\begin{array}{ccc}-1&0\\0&1\end{array}\right]`

Vertices of the new image: P'= (5,-2), Q'= (6,-3), R'= (2,-3)

Explanation:

Transformation by reflection will produce a new congruent object in different coordinate. Reflection to y-axis made by multiplying the x coordinate with -1 and keep the y coordinate unchanged. The matrix transformation for reflection across y-axis should be:
`\left[\begin{array}{ccc}-1&0\\0&1\end{array}\right]`.

To find the coordinate of the vertices after transformation, you have to multiply the vertices with the matrix. The calculation of the each vertice will be:

P'=
`\left[\begin{array}{ccc}-1&0\\0&1\end{array}\right]`
`\left[\begin{array}{ccc}-5\\-2\end{array}\right]`= (5,-2)

Q'=
`\left[\begin{array}{ccc}-1&0\\0&1\end{array}\right]`
`\left[\begin{array}{ccc}-6\\-3\end{array}\right]`= (6,-3)

R'=
`\left[\begin{array}{ccc}-1&0\\0&1\end{array}\right]`
`\left[\begin{array}{ccc}-2\\-3\end{array}\right]`= (2,-3)