# How do you find the equation of the perpendicular bisector of the segment joining the points A #(6, -3)# and B #(-2, 5)#?

We know from geometry that a surface's perpendicular bisector (p.b.)

The line that passes through its midpoint (m.p.) is known as a line segment (sgmt.) &

with respect to the sgmt.

We obtain its eqn by using the Slope-Point Form of line for the p.b.

Procedure II:=

We make use of the following p.b. of a line sgmt. geometrical property.

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To find the equation of the perpendicular bisector of the segment joining the points ( A(6, -3) ) and ( B(-2, 5) ), follow these steps:

**Find the midpoint**of the segment joining ( A ) and ( B ): [ \text{Midpoint} \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) ]

Using the coordinates of ( A ) and ( B ): [ \text{Midpoint} \left( \frac{6 + (-2)}{2}, \frac{(-3) + 5}{2} \right) ] [ \text{Midpoint} \left( 2, 1 \right) ]

**Find the slope**of the line passing through ( A ) and ( B ): [ m = \frac{y_2 - y_1}{x_2 - x_1} ]

Using the coordinates of ( A ) and ( B ): [ m = \frac{5 - (-3)}{-2 - 6} ] [ m = \frac{8}{-8} ] [ m = -1 ]

The negative reciprocal of the slope ( m ) is the slope of the perpendicular bisector.

[ m_{\text{perpendicular}} = \frac{-1}{m} ] [ m_{\text{perpendicular}} = \frac{-1}{-1} ] [ m_{\text{perpendicular}} = 1 ]

**Use the point-slope form**to find the equation of the perpendicular bisector: [ y - y_1 = m_{\text{perpendicular}}(x - x_1) ]

Using the midpoint ( (2, 1) ): [ y - 1 = 1(x - 2) ] [ y - 1 = x - 2 ] [ y = x - 1 ]

So, the equation of the perpendicular bisector of the segment joining ( A(6, -3) ) and ( B(-2, 5) ) is ( y = x - 1 ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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