prove that the point (3,0),(6,4)and (-1,3) are vertices of a right -angled isosceles triangle
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Given A(3, 0), B(6, 4) and C(–1, 3)
AB^2 = (3 – 6)^2 + (0 – 4)^2
= 9 + 16 = 25
BC^2 = (6 + 1)^2 + (4 – 3)^2
= 49 + 1 = 50
CA^2 = (–1 – 3)^2 + (3 – 0)^2
= 16 + 9 = 25
AB^2 = CA^2 ⇒ AB = CA
Triangle is isosceles
Also,
25 + 25 = 50
⇒ AB^2 + CA^2 = BC^2
Since Pythagoras theorem is verified, therefore
Triangle is a right angled triangle
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