Perpendicular intersect

[nsnr8r]

I need some help please. I'm trying to find an intersect for a graphics application. Could someone please provide an equation to solve this type of problem?

Example:
I have three points.
A= 1,1
B= 3,2
C= 2,2
Find the coordinate of the intersect of a line that passes though C and is perpendicular to segment AB.

Thanks

 

[stapel]

Plug A and B into the slope formula. This gives you the slope of AB.

Find the perpendicular slope, using the relationship between slopes of perpendicular lines.

Then use whatever formula you prefer to find the straight-line equation for the line through C with the slope you just found.

(Note: You will also need to find the equation of the line through A and B.)

Once you have the two line equations, solve the system of equations for the intersection point.

If you get stuck, please reply showing how far you have gotten. Thank you.

Eliz.

 

[nsnr8r]

Thanks. I've gotten this far,but I don't know how to find the intersection point
if:
A= 1,1
B= 3,2
C= 2,2

Solve for m:
m = (y1 - y2)/(x1 - x2) = (1-2)/(1-3) = -1/-2
m = 1/2
perp. m =-2/1

Solve for b:
1 = 1/2*1 + b
b = 1-1/2*1 = 0.5
b = 1/2

line through A and B: y = 1/2x+1/2

Find line through c with slope -2:
y = mx + b
4 = (-2)(4) + b
4 = –8 + b
b = 12
y=-2x+12

 

[jonboy]

Hello, nsnr8r!

At first I thought we would not need to find equation of a line, since you said line segment, but we definetly do.


The equation of line AB is [1]:\(\displaystyle \L \;y\,=\,\frac{1}{2}x\,+\,\frac{1}{2}\)


The equation perpendicular to [1] with \(\displaystyle \,(2,2)\,\):\(\displaystyle \L \;y\,=\,-\,2x\,+\,6\)

Solve the system:\(\displaystyle \L \;
\begin{array}{l}
y = \frac{1}{2}x + \frac{1}{2} \\
\\
\\
y = - 2x + 6 \\
\end{array}\)