Question 1203533
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A triangle has the coordinates (2, 7), (3, 5) and (1,0).

Is this a right triangle?
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Let the points be A= (2,7),  B= (3,5), C= (1,0).


Then the three vectors are

    AB = (3-2,5-7) = (1,-2)

    AC = (1-2,0-7) = (-1,-7)

    BC = (1-3,0-5) = (-2,-5)


The trianle is right-angled if and only if one of the three scalar product of these three vectors is zero.
So, calculate the scalar products

    AB * AC = 1*(-1) + (-2)*(-7) = -1 + 14 = 13;

    AB * BC = 1*(-2) + (-2)*(-5) = -2 + 10 = -8;

    AC * BC = (-1)*(-2) + (-7)*(-5) = 2 + 35 = 37.


As you see, no one scalar product is zero - so we conclude that the triangle is not a right-angled triangle.
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Solved.