Question

the points P ( 4,3) Q ( -5,-1) and T ( 2,-2) are vertices of a
(a) Equilateral triangle
(b) Isosceles triangle
(c) Scalene triangle
(d) No triangle ​

Answer 1

$\textbf{Given:}$

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

$\textbf{To find:}$

$\text{whether the given points form a triangle}$

$\textbf{Solution:}$

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

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

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

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

$PQ=\sqrt{81+16}$

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

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

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

$QT=\sqrt{49+1}$

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

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

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

$PT=\sqrt{4+25}$

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

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

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

$\boxed{\textbf{Option (c) is corrct}}$

Answer 2

Answer:

option -(c) scalene triangle.