11. (a) Prove that the points (-2, 3), (8, 3) and (6, 7) are the vertices of a right-angled triangle. Also, find the length of the hypotenuse.
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Answer: let the points be A, B and C respectively..
by distance formula
AB=√[(8+2)²+(3-3)²]
=10 units
similarly,
BC= 2√5 units
AC= 4√5 units
AC²+BC²= 20+80
=100
and AB²=100
therefore A, B, C form a right angled triangle
forming a right angle at C
(inverse of Pythagoras theorem)
Step-by-step explanation:
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