A line segment with endpoints at #(5, 5)# and #(1, 2)# is rotated clockwise by #pi/2#. What are the new endpoints of the line segment?

1 Answer
Sep 29, 2017

#6y-8x=45#

Explanation:

Slope of the line segment #m1=(y2-y1)/(x2-x1)#
#m1=(2-5)/(1-5)#
#m1=-3/-4=3/4#
Mid point of the line segment #=((5+1)/2,(5+2)/2)#
#=(3,3(1/2))#
When the line segment is rotated clock-wise by #pi/2)#,
the rotated line becomes perpendicular to the existing line segment.
Slope of rotated line #m2 = -(1/m1) = -1/(3/4)=-4/3#
Since the line segment is rotated by #pi/2# with mid point as the axis, the rotated line slope is #-(4/3)# and the mid point coordinates #(3,3(1/2))#
Equation of the rotated line is
#(y-y1)=m((x-x1)#
#(y-3(1/2))=-(4/3)(x-3)#
#(2y-7)/2=(-4x+12)/3#
#6y-21=-8x+24#
#6y+8x=45#