Question

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

Answer 1

Answer:

$(2.5, -1.3)$

Step-by-step explanation:

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

To find midpoint we use formula

$(\frac{x1+x2}{2} ,\frac{y1+y2}{2})$

(3.5,2.2) is (x1,y1)

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

Plug in all the values in the formula

$(\frac{x1+x2}{2} ,\frac{y1+y2}{2})$

$(\frac{3.5+1.5}{2} ,\frac{2.2-4.8}{2})$

$(2.5, -1.3)$ is the midpoint

Answer 2

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

Step-by-step explanation: