A triangle has corners at #(6 , 1 )#, ( 4, 2 )#, and #( 2, 8 )#. What are the endpoints and lengths of the triangle's perpendicular bisectors?
Endpoints at [
Thus, lines [1], [2], and [3] are perpendicular to AB, BC, and CA, respectively, and side BC, b, are met by line [3], which is perpendicular to AC.
We require the equations of the three perpendicular lines as well as the lines in which the sides BC and CA lie.
locating the intercepts on the BC and CA sides
Putting equations [1] and [c] together
Putting equations [2] and [c] together
Integrating the formulas [3] and [a]
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The endpoints of the perpendicular bisectors are:
 Endpoint 1: (5, 4.5)
 Endpoint 2: (4, 4)
The lengths of the perpendicular bisectors are:
 Length 1: 2.5
 Length 2: 2.236
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The endpoints of the perpendicular bisectors of a triangle are found by finding the midpoints of each side of the triangle and then finding the points perpendicular to those midpoints. Here are the steps:

Find the midpoints of each side of the triangle using the midpoint formula: Midpoint = ((\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}))

Calculate the slopes of the sides of the triangle using the formula: Slope = (\frac{y_2  y_1}{x_2  x_1})

Find the negative reciprocal of each slope to get the slope of the perpendicular bisector.

Use the slope and the midpoint to find the equation of the perpendicular bisector using the pointslope form of a line: (y  y_1 = m(x  x_1))

Calculate the endpoints of the perpendicular bisectors by plugging in the xvalues of the triangle's vertices into the equation of the perpendicular bisectors.

Once you have the endpoints of the perpendicular bisectors, you can calculate their lengths using the distance formula: Distance = (\sqrt{(x_2  x_1)^2 + (y_2  y_1)^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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