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

Answer:

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)

Step-by-step 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)