Prove that (2,-2), (-2,1) and (5,2) are the vertices of right angles triangle. find the area of the triangle and the length of the hypotenuse.
Answers
1.Use the distance formula to calculate the distance between the three points.
2. Substitute the values in the pythagoras formula as follows.
(side 1)^2 + (side 2)^2 = (side 3)^2
where ^2 implies the distance being squared,
and, side 3 is the longest side.
a.If the left hand side of the equation is equal to the right hand side of the equation, Congratulations! The given points might be the vertices of a right angled triangle. Also, the longest side is the hypotenuse.
b.If not, it isn't a right angled triangle.
3. But we're not sure as of yet if the given points indeed enclose a triangle or not, because we have not yet checked out the area of our triangle.
By using the area formula, we calculate the area of the triangle.
a. If the area is found to be a substantial amount, well and good! If condition 2.a is satisfied along with this, you have your right angled triangle!
b.If the area comes to equal 0 square units, the given points do not enclose a triangle, but are actually, collinear points.