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 Problem: line through (5,5) and perpendicular to line passing (1,-2) and (-5,2) [ Calculator, Method and examples ]Solution: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=2Slope = 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=3/2The 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=0Here B(1,-2), C(-5,2) are the given points:. x_1=1, y_1=-2, x_2=-5, y_2=2The equation of a line AB is(y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1):. (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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