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Write the equation for the perpendicular bisector of the given line segment.

A
B)
4.3x+ /
= 3x }

Write the equation for the perpendicular bisector of the given line segment. A B) 4.3x-example-1
User Vuks
by
8.1k points

1 Answer

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Answer:


y=(1)/(3)x+(5)/(3)

Explanation:

Let

A(-5,5),B(-2,-4) ----> the given segment

step 1

Find the slope AB

The formula to calculate the slope between two points is equal to


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

substitute the given values


m=(-4-5)/(-2+5)


m=(-9)/(3)


m=-3

step 2

we know that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of the slopes is equal to -1)

so

the slope of the perpendicular bisector is equal to


m_1*m_2=-1

we have


m_1=-3

substitute


(-3)*m_2=-1


m_2=(1)/(3)

step 3

Find the midpoint segment AB

A(-5,5),B(-2,-4)

The formula to calculate the midpoint between two points is equal to


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

substitute the values


M((-5-2)/(2) ,(5-4)/(2))


M(-(7)/(2) ,(1)/(2))

step 4

Find the equation of the line in point slope form


y-y1=m(x-x1)

we have


m=(1)/(3)


M(-(7)/(2) ,(1)/(2))

substitute


y-(1)/(2)=(1)/(3)(x+(7)/(2))

step 5

Convert to slope intercept form


y=mx+b

isolate the variable y


y-(1)/(2)=(1)/(3)x+(7)/(6)


y=(1)/(3)x+(7)/(6)+(1)/(2)


y=(1)/(3)x+(10)/(6)

simplify


y=(1)/(3)x+(5)/(3)

see the attached figure to better understand the problem

Write the equation for the perpendicular bisector of the given line segment. A B) 4.3x-example-1
User Arnulfo
by
7.4k points

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