2a2 + 3b2 + a2 + b2
2 answers:
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Given:
The vertices of a triangle ABC are A(-3,-4), B(16,-2) and C(13,-10).
To show:
That the triangle ABC is a right angled triangle.
Solution:
Distance formula:
The vertices of a triangle ABC are A(-3,-4), B(16,-2) and C(13,-10).
Using the distance formula, we get
Similarly,
And,
Now, add the square of two smaller sides.
Since the sum of the square of two smaller sides is equal to the square of the largest side, therefore the given triangle is a right angle triangle by using Pythagoras theorem.
Hence proved.