Question

The points a (0 6) b (-5 3) c(3 1) are the vertices of a triangle which is

Answer 1

Answer:

is a right angled triange

Answer 2

SOLUTION

TO DETERMINE

The points A(0,6), B(-5,3) and C(3,1) are the vertices of a triangle, which is

EVALUATION

Here the given points are A(0,6), B(-5,3) and C(3,1)

Now

AB

$\sf{ = \sqrt{ {(0 + 5)}^{2} + {(6 - 3)}^{2} } }$

$\sf{ = \sqrt{ {( 5)}^{2} + {( 3)}^{2} } }$

$\sf{ = \sqrt{25 + 9} }$

$\sf{ = \sqrt{34 } }$

BC

$\sf{ = \sqrt{ {(3 + 5)}^{2} + {(1 - 3)}^{2} } }$

$\sf{ = \sqrt{ {(8)}^{2} + {( - 2)}^{2} } }$

$\sf{ = \sqrt{ 64 + 4} }$

$\sf{ = \sqrt{ 68} }$

CA

$\sf{ = \sqrt{ {(3 - 0)}^{2} + {(1 - 6)}^{2} } }$

$\sf{ = \sqrt{ {(3 )}^{2} + {( - 5)}^{2} } }$

$\sf{ = \sqrt{ 9 + 25 } }$

$\sf{ = \sqrt{34} }$

Thus we see that

$\sf{ {BC}^{2} = {AB}^{2} + {CA}^{2} }$

Hence ABC is a right angled triangle

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