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Problem: line through (5,5) and perpendicular to line passing (1,-2) and (-5,2) [ Calculator, Method and examples ]

Your problem `->` line through (5,5) and perpendicular to line passing (1,-2) and (-5,2)

When two lines are perpendicular, their slopes are opposite reciprocals of one another or the product of their slopes is -1.
We shall first find the slope of `(1,-2)` and `(-5,2)`

Points are `B(1,-2), C(-5,2)`

`:. x_1=1, y_1=-2, x_2=-5, y_2=2`

Slope = `m = (y_2-y_1)/(x_2-x_1)`

`:. m = (2+2)/(-5-1)`

`:. m = (4)/(-6)`

`:. m = -2/3`

`:.` Slope`=-2/3`

`:.` Slope of perpendicular line`=3/2`

The equation of a line with slope m and passing through `(x_1,y_1)` is `y-y_1=m(x-x_1)`

Putting `(5,5)` for `(x_1,y_1)` and `m=3/2,` we get

`:. y-5=3/2(x-5)`

`:. 2(y-5)=3(x-5)`

`:. 2y -10=3x -15`

`:. 3x-2y-5=0`

Here `B(1,-2), C(-5,2)` are the given points

`:. x_1=1, y_1=-2, x_2=-5, y_2=2`

The equation of a line AB is

`:. (y+2)/(2+2)=(x-1)/(-5-1)`

`:. (y+2)/(4)=(x-1)/(-6)`

`:. (y+2)/(2)=(x-1)/(-3)`

`:. -3(y+2)=2(x-1)`

`:. -3y -6=2x -2`

`:. 2x+3y+4=0`

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