SOLUTION: show that a triangle with vertices (5,-3) (2,-6) and (1,1) is a right angled triangle. Find the area.

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Question 675162: show that a triangle with vertices (5,-3) (2,-6) and (1,1) is a right angled triangle. Find the area.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
to show that a triangle with vertices (5,-3) (2,-6) and (1,1) is a right angled triangle, first find the length of each side which is actually the distance between each given point
(5,-3) and (2,-6)
Solved by pluggable solver: Distance Formula to determine length on coordinate plane
The distance (d) between two points is given by the following formula:

d=sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29

Thus in our case, the required distance is
d=sqrt%28%282-5%29%5E2+%2B+%28-6--3%29%5E2%29=+4.24264068711928+


For more on this concept, refer to Distance formula.



(5,-3)and (1,1)
Solved by pluggable solver: Distance Formula to determine length on coordinate plane
The distance (d) between two points is given by the following formula:

d=sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29

Thus in our case, the required distance is
d=sqrt%28%281-5%29%5E2+%2B+%281--3%29%5E2%29=+5.65685424949238+


For more on this concept, refer to Distance formula.



(2,-6) and (1,1)
Solved by pluggable solver: Distance Formula to determine length on coordinate plane
The distance (d) between two points is given by the following formula:

d=sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29

Thus in our case, the required distance is
d=sqrt%28%281-2%29%5E2+%2B+%281--6%29%5E2%29=+7.07106781186548+


For more on this concept, refer to Distance formula.




a=4.24
b=5.67

c=7.07
if c%5E2=a%5E2%2Bb%5E2, then a triangle is a right angled triangle

c%5E2=a%5E2%2Bb%5E2

7.07%5E2=4.24%5E2%2B5.66%5E2

49.99=17.98%2B32
49.99=49.98
50=50.............so, a triangle is a right angled triangle



the area;
a=4.24.......height
b=5.67.......base
A=a%2Ab%2F2=%284.24%2A5.67%29%2F2=24.0408%2F2=12.0204=12