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 b) find the ar

Question 1117361: 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
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 greenestamps(13200) (Show Source): You can put this solution on YOUR website!

It's all rather elementary; I will outline the solution method and let you do the work so that you learn something from the problem.

(a) Find the equation of the line containing points A and B.
Use the slope of that line and the coordinates of point O to find the equation of the line OS, knowing that it is perpendicular to the line containing points A and B.
Solve the pair of equations simultaneously to find where the two lines intersect. The numbers work out very nicely.

(b) Use the basic formula for the area of a triangle, using AB as the base and OS as the height. The lengths of AB and OS are easy to find using the Pythagorean Theorem.

(c) The line containing points O and A is vertical, so the line containing B and T will be horizontal; that means you know the y coordinate of point T. Then use the equation of the line containing OS to find the x coordinate of point T.
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