Q. 94.2( 17 Votes )

Show that the poi

Answer :

Given: The 3 points are A(7, 10), B(-2, 5) and C(3, -4)


AB



= √106 units …..(1)


BC



= √106 units …..(2)


AC



= √212 units


From equations 1 and 2, we have


AB = BC


Therefore, Δ ABC is an isosceles triangle …..(3)


Also, AB2 = 106 units …..(4)


BC2 = 106 units …..(5)


AC2 = 212 units …..(6)


From equations 4, 5 and 6, we have


AB2 + BC2 = AC2


So, it satisfies the Pythagoras theorem.


Δ ABC is right angled triangle …..(7)


From 3 and 7, we have


Δ ABC is an isosceles right angled triangle.


Hence, proved.


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