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प्रश्न
Find the equation of the perpendicular bisector of the line joining the points A(− 4, 2) and B(6, − 4)
उत्तर
“C” is the midpoint of AB also CD ⊥ AB.
Slope of AB = `(y_2 - y_1)/(x_2 - x_1)`
= `(-4 - 2)/(6 + 4)`
= `(-6)/10`
= `-3/5`
Slope of the ⊥r AB is `5/3`
Mid point of AB = `((x_1 + x_2)/2, (y_1 + y_2)/2)`
= `((-4 + 6)/2, (2 - 4)/2)`
= `(2/2, (-2)/2)`
= (1, −1)
Equation of the perpendicular bisector of CD is
y – y1 = m(x – x1)
y + 1 = `5/3(x - 1)`
5(x – 1) = 3(y + 1)
5x – 5 = 3y + 3
5x – 3y – 5 – 3 = 0
5x – 3y – 8 = 0
Equation of the perpendicular bisector is 5x – 3y – 8 = 0
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