Question 1112872
<font face="Times New Roman" size="+2">

*[illustration RttriangleGardenCrop.jpg]


The slopes of perpendicular lines are negative reciprocals. Since the slope of the line containing the segment AB is 2, the slope of the perpendicular line containing the segment BC must be *[tex \Large -\frac{1}{2}]


Using the Point-Slope form, a line with a slope of *[tex \Large -\frac{1}{2}] passing through the point *[tex \Large \(-8,\,0\)] is given by:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ -\ 0\ =\ -\frac{1}{2}(x\ +\ 8)]


Or simplified to Slope-Intercept form:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ -\frac{1}{2}x\ -\ 4]


The equation of the line containing the segment AB is given in slope-intercept form, so just equate the two right-hand sides:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2x\ +\ 1\ =\ -\frac{1}{2}x\ -\ 4]


Solve for *[tex \Large x] and then substitute back into either equation to find *[tex \Large y], then verify that the point of intersection is indeed *[tex \Large (-2,-3)].


Substitute *[tex \Large x\ =\ 4] into both equations to find the coordinates of the other two points.


Then use the distance formula:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ d\ =\ \sqrt{\(x_1\ -\ x_2\)^2\ +\ \(y_1\ -\ y_2\)^2}]


Three times giving you the lengths of the three sides.  Add the measures of the three sides to get the perimeter.  Leave your answer in radical form to express the answer exactly.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
<img src="http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg">
*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  

</font>