How do I find the equation of a perpendicular bisector of a line segment with the endpoints #(2, 4)# and #(6, 4)#?
This could be rephrased as
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To find the equation of the perpendicular bisector of a line segment with endpoints (2, 4) and (6, 4), follow these steps:

Find the midpoint of the line segment using the midpoint formula: [ \text{Midpoint} = \left( \frac{{x_1 + x_2}}{2}, \frac{{y_1 + y_2}}{2} \right) ]

Calculate the slope of the line segment connecting the given endpoints using the slope formula: [ m = \frac{{y_2  y_1}}{{x_2  x_1}} ]

Find the negative reciprocal of the slope found in step 2. This will be the slope of the perpendicular bisector.

Use the pointslope form of a line equation, using the midpoint found in step 1 and the slope found in step 3: [ y  y_1 = m_{\text{perpendicular}}(x  x_1) ]

Substitute the midpoint coordinates and the perpendicular slope into the pointslope form to find the equation of the perpendicular bisector.
Let's go through the steps:

Midpoint: [ \text{Midpoint} = \left( \frac{{2 + 6}}{2}, \frac{{4 + 4}}{2} \right) = (2, 0) ]

Slope of the line segment: [ m = \frac{{4  (4)}}{{6  (2)}} = \frac{8}{8} = 1 ]

Slope of the perpendicular bisector: [ m_{\text{perpendicular}} = \frac{1}{m} = 1 ]

Using the pointslope form with the midpoint (2, 0) and the perpendicular slope (1): [ y  0 = 1(x  2) ]

Simplify the equation: [ y = x + 2 ]
Therefore, the equation of the perpendicular bisector of the line segment with endpoints (2, 4) and (6, 4) is ( y = x + 2 ).
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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