The Equation of the Perpendicular Bisector of Line Segment Joining Points A(4,5) And B(-2,3) IS - Mathematics

The equation of the perpendicular bisector of line segment joining points A(4,5) and B(-2,3) is

(a) 2x – y +7=0

(b) 3x +2 y – 7=0

(c) 3x – y – 7 =0

(d) 3x + y – 7=0



(d) 3x + y – 7=0

Explanation:

Any point (x, y) of perpendicular bisector will be equidistant from A & B.

By, Symmetry

AP = BP

= `\sqrt{(x-4)^{2}+(y-5)^{2}}` = `\sqrt{(x-(-2)^{2}+(y-3)^{2}`

= `\sqrt{(x-4)^{2}+(y-5)^{2}}` = `\sqrt{(x + 2)^{2}+(y-3)^{2}`

By squaring both side

= `(x-4)^{2} + (y-5)^{2} = (x+2)^{2} +(y-3)^{2}`

= `x^{2}+16-8x+y^{2}+25-10y` = `x^{2}+ 4-4x+y^{2}+9-6y`

= `-8x-10y + 41` = `4x - 6y + 13`

= `-8x-10y + 41 - 4x + 6y - 13` = 0

= `-8x- 4x -10y+ 6y+ 41- 13` = 0

= 12x + 4y - 28 = 0

= 4 (3x + y - 7) = 0

= 3x + y - 7 = `0/4`

= 3x + y - 7 = 0







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