Question

In the following examples, can the segment joining the given points form a triangle? If triangle is formed, state the type of the triangle considering sides of the triangle. 

L (6, 4), M (-5, -3), N (-6, 8) 

Answer 1

 By distance formula,

d(L,M) = \(\sqrt {(x_2-x_1)^2 + (y_2 - y_1)^2}\)

= \(\sqrt {(-5-6)^2 + (-3- 4)^2}\)

= \(\sqrt {(-11)^2 + (-7)^2}\)

= \(\sqrt {121+49} \)

∴ d(L, M) = \(\sqrt {170 } \)     ....(i)

∴ d ( M , N ) + d ( L , N ) > d ( L , M )

∴ Points L, M, N are non collinear points. We can construct a triangle through 3 non collinear points. 

∴ The segment joining the given points form a triangle. 

Since MN ≠ LN ≠ LM 

∴ ∆LMN is a scalene triangle. 

∴ The segments joining the points L, M and N will form a scalene triangle.