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Question

Find the equation of the right bisector of the line segment joining the points A (1, 0) and B (2, 3).


Solution

The given piont are A (1, 0) and B (2, 3)Let M be the midpoint of AB.Coordinates of M=(1+22,0+32)=(32,32)

And, slope of AB=3021=3Let m be the slope of the perpendicular bisector of the line joining the points A (1, 0) and B (2, 3) m× Slope of AB=1 m×3=1 m=13So, the equation of the line that passesthrough M(32,32) and has slope13 isy32=13(x32) x+3y.6=0Hence, the equation of the right bisector of the line segment joining the points A (1, 0) and B (2, 3) is x + 3y - 6 = 0P.Q. Find the equation of the line passing through (1, 2) and making angle of 30 with y=axis..Equation of the line passing through (x1, y1) and making angle θ with the x-axis is,(yy1)=tanθ (xx1)Here, (x1,y1)=(1, 2), angle with y-axis is 30 angle with x-axis isθ=9030=60(yy1)=tanθ (xx1)(y2)=(tan 60)(x1)y2=3x33xy+23=0

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