SOLUTION: Plot each point and from the right triangle ABC. Verify that the triangle is a right triangle.Find its area. A=(2,-6); B=(0,-6); C=(2,1)

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Question 985219: Plot each point and from the right triangle ABC. Verify that the triangle is a right triangle.Find its area. A=(2,-6); B=(0,-6); C=(2,1)
Answer by MathLover1(20850) About Me  (Show Source):
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A=(2,-6); B=(0,-6); C=(2,1)
Plot each point and from the right triangle ABC.

to verify that the triangle is a right triangle, find the length of each side and prove that
%28BC%29%5E2=%28BA%29%5E2%2B%28AC%29%5E2
find BC
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%282-0%29%5E2+%2B+%281--6%29%5E2%29=+7.28010988928052+


For more on this concept, refer to Distance formula.


find AC
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%282-2%29%5E2+%2B+%281--6%29%5E2%29=+7+


For more on this concept, refer to Distance formula.


find BA
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%280-2%29%5E2+%2B+%28-6--6%29%5E2%29=+2+


For more on this concept, refer to Distance formula.



so, BC=7.2801098828052=7.28, AC=7, and BA=2
%28BC%29%5E2=%28BA%29%5E2%2B%28AC%29%5E2
%287.2801098828052%29%5E2=2%5E2%2B7%5E2
52.9984=4%2B49
53=53
now find its area:
A=%281%2F2%29%28BA%29%28AC%29
A=%281%2F2%292%2A7
A=%281%2Fcross%282%29%29cross%282%29%2A7
A=7