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How do you work out the equation for the perpendicular bisector of the straight line joining h k and 3h -5k showing details of your work?
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JudyFirst find the midpoint and slope of points (h, k) and (3h, -5k)
Midpoint = (h+3h)/2, (6k+k)/2 = (2h, -2k)
Slope = (-5k-k)/(3h-h) = -6k/2h = -3k/h
Then find the perpendicular slope which is the positive reciprocal of -3k/h which is h/3k
Then substitute these values into the formula of y-y1 = m(x-x1) :-
y-(-2k) = h/3k(x -2h)
y = hx/3k -2h2/3k -2k
Multiply all terms by 3k and the perpendicular bisector equation can be expressed in the form of :-
hx -3ky -2h2 -6k2 = 0
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What is -6x plus 2y equaling -2 on a graph look like?
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