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The points $A(1,2), B(2,4)$ and $C(4,8)$ form a/an
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The correct answer is:
straight line
Given points, $A(1,2), B(2,4), C(4,8)$
$A B=\sqrt{(2-1)^{2}+(4-2)^{2}}=\sqrt{1+4}=\sqrt{5}$
$B C=\sqrt{(4-2)^{2}+(8-4)^{2}}=\sqrt{4+16}=\sqrt{20}$
$C A=\sqrt{(1-4)^{2}+(2-8)^{2}}=\sqrt{9+36}=\sqrt{45}$
Slope of $A B=\frac{4-2}{2-1}=2$
Slope of $B C=\frac{8-4}{4-2}=2$
Slope of $C A=\frac{2-8}{1-4}=2$
So, the three points form a straight line or three points are collinear.
$A B=\sqrt{(2-1)^{2}+(4-2)^{2}}=\sqrt{1+4}=\sqrt{5}$
$B C=\sqrt{(4-2)^{2}+(8-4)^{2}}=\sqrt{4+16}=\sqrt{20}$
$C A=\sqrt{(1-4)^{2}+(2-8)^{2}}=\sqrt{9+36}=\sqrt{45}$
Slope of $A B=\frac{4-2}{2-1}=2$
Slope of $B C=\frac{8-4}{4-2}=2$
Slope of $C A=\frac{2-8}{1-4}=2$
So, the three points form a straight line or three points are collinear.
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