A line segment has endpoints at #(6 ,5 )# and #(2 ,7 )#. If the line segment is rotated about the origin by # pi #, translated horizontally by # 2 #, and reflected about the x-axis, what will the line segment's new endpoints be?

1 Answer
Yonas Yohannes
Jan 30, 2016

#(-4, 7); (0, 7) #

Explanation:

Use the Rotation, Translation and Reflection mattrix. But this a special case so you can do it in your head.
#vec(V') = M_(R(theta)) vec(V)#
#(-x_1, -y_1) = M_(R(theta))(x_1, y_1) #
#(-6, -7); (-2,-7) #

#vec(V'') = M_(T(2)) vec(V')#
#(-x_1 + 2, -y_1) = M_(T(2)) (-x_1, -y_1) #
#(-4, -7); (0,-7) #

#vec(V') = M_(RF(x) vec(V)#
#(-x_1 + 2, y_1) =M_(RF(x))(-x_1+2, -y_1) #
#(-4, 7); (0, 7) #

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