# Let #P(a,b) and Q(c,d)# be two points in the plane. Find the equation of the line #l# that is the perpendicular bisector of the line segment #bar(PQ)#?

Equation of line

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The equation of the perpendicular bisector of the line segment ( \overline{PQ} ) can be found using the midpoint formula and the negative reciprocal of the slope of ( \overline{PQ} ).

First, find the midpoint of ( \overline{PQ} ) using the midpoint formula: [ M\left(\frac{a+c}{2}, \frac{b+d}{2}\right) ]

Then, find the slope of ( \overline{PQ} ) using the formula: [ m_{PQ} = \frac{d - b}{c - a} ]

The negative reciprocal of ( m_{PQ} ) is ( -\frac{1}{m_{PQ}} ). This represents the slope of the perpendicular bisector.

Using the point-slope form of a line, where ( (x_1, y_1) ) is a point on the line and ( m ) is the slope: [ y - y_1 = m(x - x_1) ]

Substitute ( M\left(\frac{a+c}{2}, \frac{b+d}{2}\right) ) for ( (x_1, y_1) ) and ( -\frac{1}{m_{PQ}} ) for ( m ). Then, simplify to find the equation of the perpendicular bisector.

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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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