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4 votes
What s the midpoint of the line segment with endpoints (3.5,2.2) and (1.5,-4.8)

User Buboh
by
7.8k points

2 Answers

4 votes

Answer:

First, you must find the midpoint of the segment, the formula for which is

(

x

1

+

x

2

2

,

y

1

+

y

2

2

)

. This gives

(

5

,

3

)

as the midpoint. This is the point at which the segment will be bisected.

Next, since we are finding a perpendicular bisector, we must determine what slope is perpendicular to that of the existing segment. To determine the segment's slope, we use the slope formula

y

2

y

1

x

2

x

1

, which gives us a slope of

5

.

Perpendicular lines have opposite and reciprocal slopes. The opposite reciprocal of

5

is

1

5

.

We now know that the perpendicular travels through the point

(

5

,

3

)

and has a slope of

1

5

.

Solve for the unknown

b

in

y

=

m

x

+

b

.

3

=

1

5

(

5

)

+

b

3

=

1

+

b

2

=

b

Therefore, the equation of the perpendicular bisector is

y

=

1

5

x

+

2

.

Related questions

What is the midpoint of the line segment joining the points (7, 4) and (-8, 7)?

How would you set up the midpoint formula if only the midpoint and one

Explanation:


User Seferov
by
8.1k points
3 votes

Answer:


(2.5, -1.3)

Explanation:

the midpoint of the line segment with endpoints (3.5,2.2) and (1.5,-4.8)

To find midpoint we use formula


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

(3.5,2.2) is (x1,y1)

(1.5,-4.8) is (x2,y2)

Plug in all the values in the formula


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


((3.5+1.5)/(2) ,(2.2-4.8)/(2))


(2.5, -1.3) is the midpoint

User Oliver Jan Krylow
by
8.8k points

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