SOLUTION: a triangle has an area of 6 square units. I t has vertices with coordinates(1,-3),(4,2) and a point on the x-axis. find all possible coordinates for this point

Algebra ->  Matrices-and-determiminant -> SOLUTION: a triangle has an area of 6 square units. I t has vertices with coordinates(1,-3),(4,2) and a point on the x-axis. find all possible coordinates for this point       Log On


   

Question 390390: a triangle has an area of 6 square units. I t has vertices with coordinates(1,-3),(4,2) and a point on the x-axis. find all possible coordinates for this point
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The area of any triangle having vertices (a,b), (c,d), (e,f) is given by the absolute value of
det%28%28matrix%283%2C3%2C+a%2Cb%2C1%2Cc%2Cd%2C1%2C+e%2Cf%2C+1%29%29%29%2F2. Hence we want absolute value of

det%28%28matrix%283%2C3%2C+1%2C-3%2C1%2C4%2C2%2C1%2C+x%2Cy%2C+1%29%29%29%2F2+ = 6 or , after evaluating and simplifying the determinant,
|3y - 5x + 14| = 12. This is equivalent to 2 linear equations, namely
3y - 5x = -2, OR
3y - 5x = -26.
Any point with coordinates satisfying either equation would form with the other two points a triangle of area 6.