Question 870653: Dear Math Tutor,
Show that the triangle formed by the points (-2,5), (1,3) and (5,9) is right angled.
Now in my textbook they give me this example: Show that the points (0,5), (-1,2), (4,7) and (5,0) form a rhombus.
The midpoints of the diagonals are ((0+4)/2,(-5+7)/2)), or (2,1). and ((-1+50/2,(2+0)/2)), or (2,1). As these are the same point, the quadrilateral is a parallelogram.
The gradients of the diagonals are (7-(-5)/(4-0)=3 and (0-2)/(5-(-1)= -1/3. As the product of the gradients is -1, the diagonals are perpendicular. Therefore the parallelogram is a rhombus.
So they dont give me an example on how to show that a triangle is right angled, therefore i am now confused. Do i find the midpoints, gradients, equation of lines? And how will i know at the end of the day that its a right angled triangle. Please help me with process and methods.
Would greatly appreciate your help.
With gratitude,
Nats
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! Show that the triangle formed by the points (-2,5), (1,3) and (5,9) is right angled.
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One way is to use the distance formula to see if the Pythagorean theorem holds for the lengths of the 3 sides:
A=(-2,5)
B=(1,3)
C=(5,9)
AB = sqrt(3^2+2^2) = sqrt(13) = a
BC = sqrt(4^2+6^2) = sqrt(52) = b
AC = sqrt(7^2+4^2) = sqrt(65) = c
a^2 + b^2 = 13 + 52 = 65 = c^2
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