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Line p is the perpendicular bisector of MN. Write the equation of line p in slope-intercept form.

Line p is the perpendicular bisector of MN. Write the equation of line p in slope-example-1
User Josh At The Nerdery
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1 Answer

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18 votes

Line p is perpendicular bisector of line MN. This means that it divides line MN equally. Thus, point B is the midpoint of line MN. Thus, we would find the midpoint of line MN by applying the midpoint formula which is expressed as

(x1 + x2)/2, (y1 + y2)/2

Looking at the given points of line MN,

x1 = - 5, y1 = 2

x2 = 7, y2 = - 1

Midpoint = (- 5 + 7)/2, (2 + - 1)/2

Midpoint = 2/2, 1/2

Midpoint = 1, 1/2

We would find the slope of line MN. The formula for finding slope is expressed as

m = (y2 - y1)/(x2 - x1)

Looking at the given points of line MN,

x1 = - 5, y1 = 2

x2 = 7, y2 = - 1

m = (- 1 - 2)/(7 - - 5) = - 3/(7 + 5) = - 3/12 = - 1/4

If two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line. This means that the slope of line p is 4/1 = 4

Thus, line p is passing through point (1, 1/2) and has a slope of 4

The equation of a line in the slope intercept form is expressed as

y = mx + c

where

m represents slope

c represents y intercept

To determine the equation of line p, we would substitute m = 4, x = 1 and y = 1/2 into the slope intercept equation. It becomes

1/2 = 4 * 1 + c

1/2 = 4 + c

c = 1/2 - 4

c = - 7/2

Substituting m = 4 and c = - 7/2 into the slope intercept equation, the equation of line p would be

y = 4x - 7/2

User Bokibeg
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