SOLUTION: The vertices of triangle OAB are the points O (0,0), A (0,2) and B (3,-1),
a) The point S is on AB such that OS is perpendicular to AB. Find the coordinates of S, and show this po
Algebra.Com
Question 1117365: The vertices of triangle OAB are the points O (0,0), A (0,2) and B (3,-1),
a) The point S is on AB such that OS is perpendicular to AB. Find the coordinates of S, and show this point on your diagram.
b) Find the area of triangle OAB.
c) The line through the point B, perpendicular to OA, meets OS produced at T. Find the coordinates of T.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
.
Equation of the line containing the segment 
. Use the Two-Point Form:
}{0\ -\ 3}(x\ -\ 0))
By inspection, the slope of this line is -1.
Since the slopes of perpendicular lines are negative reciprocals, the slope of the line containing the segment 
must be 
Using the Point-Slope form, the equation of the line containing the segment 
is
Solving the 2X2 system of equations:
Hence, the point of intersection is )
Using the distance formula, find the measures of segments and
^2\ +\ (2\,-\,(-1)\)^2}\ =\ \sqrt{9\ +\ 9}\ =\ 3\sqrt{2})
^2\ +\ (0\,-\,1\)^2}\ =\ \sqrt{1\ +\ 1}\ =\ \sqrt{2})
The area of a triangle is given by one-half the base times the altitude:
\(\sqrt{2}\)\ =\ \frac{1}{2}\,\cdot\,3\,\cdot\,2\ =\ 3)
John
My calculator said it, I believe it, that settles it
RELATED QUESTIONS
The vertices of triangle OAB are the points O (0,0), A (0,2) and B (3,-1)
a) the... (answered by greenestamps)
The vertices of a triangle OAB are O (0,0) A(0,2) B(3,-1) . A point S on AB is such that... (answered by Cromlix)
Given triangle OAB with vertices O(0, 0), A(5, 2), and B(a, b), let AP and BQ be the... (answered by greenestamps)
I NEED HELP. PLEASE HELP ME ASAP. THANKS BEFORE :)
1) The straight line with equation... (answered by richard1234)
The coordinates of O, A and B are O(0,0) , A(5,0) , B(7,8). Find
a) The gradient of AB,
(answered by Edwin McCravy)
Points O(0,0) and B(0,3) below lie in the standard (x,y) coordinate plane. The collection (answered by josgarithmetic)
The position of an ant and a spider in a room are A(2,3,5) and S(6,0,8) Determine the... (answered by math_tutor2020,mananth)
In the diagram, three vertices of parallelogram ORST are O(0, 0), R(b, d), and T(a,0).... (answered by Edwin McCravy)
Find the coordinates of P such that P is a point on AB, A(0,6), B(6,0), AP:AB=2:1
(answered by greenestamps,Edwin McCravy,ikleyn,AnlytcPhil)