# Thread: Analytic Geometry

1. ## Analytic Geometry

Help
Determine an equation for the right bisector of the line segment joining (-1,2) and (3,6)
any ideas

2. Originally Posted by diva25
Help
Determine an equation for the right bisector of the line segment joining (-1,2) and (3,6)
any ideas
The midpoint of the line segment will give you a point on the line you want.

$\frac{- 1}{\text{Gradient of line segment}}$ will give you the gradient of the line you want.

Use these two things to get the equation of the line you want.

3. ## Mr Fantastic

Thank you, it's been 30 years since I've done math and I have to prove myself I guess, to be able to take a calculus course and this was just one of my 100 questions.

4. Originally Posted by diva25
Help
Determine an equation for the right bisector of the line segment joining (-1,2) and (3,6)
any ideas
midpoint=(x1+x2/2 + y1+y2/2)
= (-1+3/2 + 2+6/2)
= (2/2 + 8/4)
midpoint= (1,2)

now you must find the slope of the line
slope= y2-y1/x2-x1
=6-2/3-(-1)
=4/4
=1
slope=1

now since its a right bisector it must be the negative reciprocal, therefore the slope of the line you want is -1

now simply plug the values into the equation of a line first putting it into the equation y- k = m(x - h)

then solve the point slope equation for y to get y=mx+b

can you finish it?