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Kipish [7]
3 years ago
7

Identify the equation in point-slope form for the perpendicular bisector of the segment with endpoints J(−24,−4) and K(−4,6).

Mathematics
1 answer:
natima [27]3 years ago
5 0

Given:

Endpoints of a segment are J(−24,−4) and K(−4,6).

To find:

The equation in point-slope form for the perpendicular bisector of JK.

Solution:

Slope of JK is

m=\dfrac{y_2-y_1}{x_2-x_1}

m=\dfrac{6-(-4)}{-4-(-24)}

m=\dfrac{6+4}{-4+24}

m=\dfrac{10}{20}

m=\dfrac{1}{2}

Product of slopes of two perpendicular lines is -1. So, product of perpendicular line of JK is -2.

Perpendicular bisector of JK passes through the midpoint of JK.

Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)

Midpoint=\left(\dfrac{-24-4}{2},\dfrac{-4+6}{2}\right)

Midpoint=\left(\dfrac{-28}{2},\dfrac{2}{2}\right)

Midpoint=\left(-14,1\right)

Point slope form:

y-y_1=m(x-x_1)

where, m is slope.

Perpendicular bisector of JK passes through (-14,1) with slope -2. So, the point slope form of JK is

y-1=-2(x-(-14))

y-1=-2(x+14)

Therefore, the correct option is D.

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Answer:

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Step-by-step explanation:

The picture of the question in the attached figure

we know that

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therefore

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