How do you find the equation of the perpendicular bisector of the points #(1,4)# and #(5,-2)#?
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To find the equation of the perpendicular bisector of the line segment between the points ((1, 4)) and ((5, -2)):
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Find the midpoint of the line segment using the midpoint formula: [ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) ]
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Calculate the slope of the line passing through the two given points using the slope formula: [ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} ]
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Determine the negative reciprocal of the slope found in step 2 to obtain the slope of the perpendicular bisector.
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Use the midpoint found in step 1 and the slope obtained in step 3 to write the equation of the perpendicular bisector using the point-slope form: [ y - y_1 = m_{\text{perpendicular}}(x - x_1) ]
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Simplify the equation to obtain the final form.
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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.
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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