Question

बिन्दु P(4, 3), Q(-5, 1) और T(2, -2) निम
न त्रिभुज के शीर्ष है
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Answer 1

$\underline{\textbf{Given:}}$

$\textsf{Points are P(4,3), Q(-5-1), T(2,-2)}$

$\underline{\textsf{To find:}}$

$\textsf{whethere the given points form a triangle}$

$\underline{\textsf{Solution:}}$

$\textsf{First we find the lengths PQ,QT,PT }$

$PQ=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

$PQ=\sqrt{(4+5)^2+(3+1)^2}$

$PQ=\sqrt{9^2+4^2}$

$PQ=\sqrt{81+16}$

$\bf\,PQ=\sqrt{97}$

$QT=\sqrt{(-5-2)^2+(-1+2)^2}$

$QT=\sqrt{(-7)^2+1^2}$

$QT=\sqrt{49+1}$

$\bf\,QT=\sqrt{50}$

$PT=\sqrt{(4-2)^2+(3+2)^2}$

$PT=\sqrt{2^2+5^2}$

$PT=\sqrt{4+25}$

$\bf\,PT=\sqrt{29}$

$\implies\bf\,PQ{\neq}QT{\neq}PT$

$\therefore\textsf{The given points P,Q and T form a scalene triangle}$