Question

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?

Answer 1

`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`