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Maths-

General

Easy

Question

The points $open parentheses 0 comma fraction numerator 8 over denominator 3 end fraction close parentheses comma left parenthesis 13 right parenthesis text and end text left parenthesis 8230 right parenthesis$

form an obtuse-angled triangle.
form an acute-angled triangle.
form a right-angled triangle.
lie on a straight line.

The correct answer is: lie on a straight line.

$A identical to open parentheses 0 comma fraction numerator 8 over denominator 3 end fraction close parentheses comma B identical to left parenthesis 13 right parenthesis comma C identical to left parenthesis 8230 right parenthesis$
$text Slope of end text A B equals fraction numerator 3 minus 8 divided by 3 over denominator 1 minus 0 end fraction equals fraction numerator 1 over denominator 3 end fraction comma text Slope of end text B C equals fraction numerator 30 minus 3 over denominator 82 minus 1 end fraction equals fraction numerator 27 over denominator 81 end fraction equals fraction numerator 1 over denominator 3 end fraction$
Therefore, A, B, C lie on a straight line.

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