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

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 (x1, y1) and

(x2, y2) is given by

the slope of the line AB (m1) =

the slope of the line BC (m2) =

the slope of the line CA (m3) =

Now, m1 m3 = -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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