How do you find the equation in slope-intercept form of the line that is perpendicular to AB and passes through the midpoint of AB. Let A = (-6,2) and B = (4,-10)?

1 Answer
Apr 9, 2017

y=56x196

Explanation:

The mid point is the mean value as you read left to right on the x-axis.

Point A Pa(xa,ya)=(6,2)
Point B Pb(xb,yb)=(4,10)

Let the mean point be Pm(xm,ym)
Let the gradient of the line between PaandPb be m

Note that the gradient of the perpendicular line will be 1m

We read from xa to xb

Determine the mid point

xm=xb+xa2=4+(6)2=1

ymyb+ya2=2+(10)2=4

Pm(xm,ym)=(1,4)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Determine the gradient (slope) of the perpendicular line

m=change in ychange in xybyaxbxa=1024(6)=1210=65

Thus 1m=+56
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Determine the equation of the perpendicular line
Found that y=1mx+c is:

y=56x+c .................Equation(1)

We know that this passes through the point
Pm(xm,ym)=(1,4)

So by substitution into Equation(1) we have:

4=56(1)+c

c=4+56=316=196 giving:

y=56x196
Tony BTony B