Given the points (2, 3) and (6,5), find the equation for the perpendicular bisector.

Explanation:

a perpendicular bisector, bisects a line segment at

right angles

to obtain the equation we require slope and a point on it

find the midpoint and slope of the given points

midpoint

=

[

1

2

(

1

+

5

)

,

1

2

(

4

−

2

)

]

midpoint

=

(

3

,

1

)

←

point on bisector

calculate the slope m using the

gradient formula

∙

x

m

=

y

2

−

y

1

x

2

−

x

1

let

(

x

1

,

y

1

)

=

(

1

,

4

)

and

(

x

2

,

y

2

)

=

(

5

,

−

2

)

⇒

m

=

−

2

−

4

5

−

1

=

−

6

4

=

−

3

2

given a line with slope m then the slope of a line

perpendicular to it is

∙

x

m

perpendicular

=

−

1

m

⇒

m

perpendicular

=

−

1

−

3

2

=

2

3

←

slope of bisector

using

m

=

2

3

and

(

x

1

,

y

1

)

=

(

3

,

1

)

then

y

−

1

=

2

3

(

x

−

3

)

←

in point-slope form

⇒

y

−

1

=

2

3

x

−

2

⇒

y

=

2

3

x

−

1

←

in slope-intercept form

Step-by-step explanation:

Step-by-step explanation:

Given that ,

Interval length = 3-0 =3

No of intervals= 6

Hence the end points are

Right end points are

x  0.511.522.53total

f(x)  -2.875-5-5.625-40.6259-7.875

Integral value  0.5*(-7.875)-3.9375      

So Riemann sum is -3.9375

= -3.938