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30 POINTS AND BRAINLIEST
PLEASE HELP ASAP Which of the following represents a rotation of ΔXYZ, which has vertices X (−4, 7), Y (6, 2), and Z (3, −8), about the origin by 90°? A. X (−7, −4) Y (−2, 6) Z (8, 3) B. X (7, −4) Y (−2, 6) Z (3, −8) C. X (7, −4) Y (−2, 6) Z (−3, 8) D. X (−7, −4) Y (6, −2) Z (−8, 3)

Respuesta :

gustanika
We could find the rotation point using matrix [tex] \left[\begin{array}{ccc}0&-1\\1&0\end{array}\right] [/tex]

X(-4,7) is rotated to (0, 90°)
X' = [tex] \left[\begin{array}{ccc}0&-1\\1&0\end{array}\right] \left[\begin{array}{ccc}-4\\7\end{array}\right] [/tex]
X' = [tex] \left[\begin{array}{ccc}(0\times-4)-1\times7\\(1\times-4)-0\times7\end{array}\right] [/tex]
X' = [tex] \left[\begin{array}{ccc}-7\\-4\end{array}\right] [/tex]
X' = (-7,-4)

Y(6,2) is reflected to (0,90°)
Y' = [tex] \left[\begin{array}{ccc}0&-1\\1&0\end{array}\right] \left[\begin{array}{ccc}6\\2\end{array}\right] [/tex]
Y' = [tex] \left[\begin{array}{ccc}(0\times6)-1\times2\\(1\times6)-0\times2\end{array}\right] [/tex]
Y' = [tex] \left[\begin{array}{ccc}-2\\6\end{array}\right] [/tex]
Y' = (-2,6)

Z(3,-8) is reflected to (0,90°)
Z' = [tex] \left[\begin{array}{ccc}0&-1\\1&0\end{array}\right] \left[\begin{array}{ccc}3\\-8\end{array}\right] [/tex]
Z' = [tex] \left[\begin{array}{ccc}(0\times3)-1\times-8\\(1\times3)-0\times-8\end{array}\right] [/tex]
Z' = [tex] \left[\begin{array}{ccc}8\\3\end{array}\right] [/tex]
Z' = (8,3)

See image attached
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