Q10 of 169 Page 644

Show that the points A(1, 1), B(-1, -1) and C(-√3, √3) are the vertices of an equilateral triangle each of whose sides is 22 units.

Given: The 3 points are A(1, 1), B(-1, -1) and C(-√3, √3).


AB



= 2√2 units …..(1)


BC



= 2√2 units …..(2)


AC



= 2√2 units …..(3)


From equations 1, 2 and 3, we have


AB = BC = AC = 2√2 units.


Therefore, Δ ABC is an equilateral triangle each of whose sides is 2√2 units.


Hence, proved.


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