A) isosceles triangles
B) equilateral triangle
C) straight line
D) right angled triangle
Correct Answer: C
Solution :
Given points, \[A\,(1,2),B\,(2,4),C\,(4,8)\] \[AB=\sqrt{{{(2-1)}^{2}}+{{(4-2)}^{2}}}=\sqrt{1+4}=\sqrt{5}\] \[BC=\sqrt{{{(4-2)}^{2}}+{{(8-4)}^{2}}}=\sqrt{4+16}=\sqrt{20}\] \[CA=\sqrt{{{(1-4)}^{2}}+{{(2-8)}^{2}}}=\sqrt{9+36}=\sqrt{45}\] Slope of \[AB=\frac{4-2}{2-1}=2\] Slope of \[BC=\frac{8-4}{4-2}=2\] Slope of \[CA=\frac{2-8}{1-4}=2\] So, the three points form a straight line or three points are collinear.
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