Q. 63.9( 111 Votes )

# Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and (–1, –1) are the vertices of a right-angled triangle.

Answer :

The vertices of the given triangle are (4, 4), (3, 5) and (–1, –1).

The slope (m) of the line non-vertical line passing through the point (x_{1}, y_{1}) and

(x_{2}, y_{2}) is given by

∴ the slope of the line AB (m_{1}) =

the slope of the line BC (m_{2}) =

the slope of the line CA (m_{3}) =

Now, m_{1} m_{3} = -1

⇒ Lines AB and CA are perpendicular to each other

∴ given triangle is right-angled at A (4, 4)

And the vertices of the right-angled ∆ are (4, 4) , (3, 5) and (-1, -1)

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