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

$\boxed{\rm{\orange{Given \longrightarrow }}}$

⇢Points are P(4,3), Q(-5-1), T(2,-2)

$\boxed{\rm{\red{To\:Find\longrightarrow }}}$

⇢whether the given points form a triangle

$\boxed{\rm{\pink{solution \longrightarrow }}}$

⇢First we find the lengths $PQ,QT,PT$

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

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

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

$PQ=\sqrt{81+16}$

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

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

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

$QT=\sqrt{49+1}$

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

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

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

$PT=\sqrt{4+25}$

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

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

∴The given points P,Q and T form a scalene triangle

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

Answer 2

• scalene triangle is a triangle in which all three sides have different lengths. Also the angles of a scalene triangle have different measures. Some right triangles can be a scalene triangle when the other two angles or the legs are not congruent.
• Options C is correct answer
• scalene triangle