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 ->  Linear-equations -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!


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Equation of the line containing the segment . Use the Two-Point Form:





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





The area of a triangle is given by one-half the base times the altitude:




John

My calculator said it, I believe it, that settles it