A line segment with endpoints at $(5, 5)$ $(5, 5)$ and $(1, 2)$ $(1, 2)$ is rotated clockwise by $\frac{π}{2}$ $pi/2$ . What are the new endpoints of the line segment?

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A line segment with endpoints at $(5, 5)$ $(5, 5)$ and $(1, 2)$ $(1, 2)$ is rotated clockwise by $\frac{π}{2}$ $pi/2$ . What are the new endpoints of the line segment?

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Answer 1 · 2017-09-29T02:41:51

$6 y - 8 x = 45$ $6y-8x=45$

Explanation:

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

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A line segment with endpoints at $(5, 5)$ $(5, 5)$ and $(1, 2)$ $(1, 2)$ is rotated clockwise by $\frac{π}{2}$ $pi/2$ . What are the new endpoints of the line segment?

1 Answer

Explanation:

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A line segment with endpoints at $(5, 5)$ $(5, 5)$ and $(1, 2)$ $(1, 2)$ is rotated clockwise by $\frac{π}{2}$ $pi/2$ . What are the new endpoints of the line segment?