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:

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)

step-by-step explanation:

sry but any answer choices