Question

State True or False: Without using the Pythagoras theorem, we can not show that the points $(4,4),(3,5)$ and $(-1,-1)$ are the vertices of a right-angled triangle.

• A. True
• B. False

Answer 1

The correct option is B False

We can check if triangle is right angled or not without using pythagoras.

Using slope method ($\because$ product of slopes of perpendicular lines $=-1$)

$letA(4,4),B(3,5),\&C(-1,-1)$

$Slopes:AB=\frac{5-4}{3-4}=-1;BC=\frac{-1-5}{-1-3}=\frac{-3}{2};AC=\frac{-1-4}{-1-4}=1$

$SlopeofAB\times AC=-1$

$\therefore$ $AB$ and $AC$ are perpendicular.

Hence, $\Delta ABC$ is a right angled triangle,right angled at $A.$