Question

without using Pythagoras Theorem show that the points (4,4),(3,5) and (-1,-1) at the vertices of the right angle triangle

Answer 1

hope it will satisfy
there is a formula written

Answer 2

Answer and Explanation:

To show : Without using Pythagoras Theorem show that the points (4,4),(3,5) and (-1,-1) at the vertices of the right angle triangle ?

Solution :

If we show that line drawn by points is perpendicular then it form a right angle triangle.

If slope of two lines multiple is -1 then they are perpendicular.

Slope of the points A= (4,4), B= (3,5) and C=(-1,-1)

Slope formula,

$m=\frac{y_2-y_1}{x_2-x_1}$

Slope of AB, A= (4,4), B= (3,5)

$m_1=\frac{5-4}{3-4}$

$m_1=\frac{1}{-1}$

$m_1=-1$

Slope of BC, B= (3,5) and C=(-1,-1)

$m_2=\frac{-1-5}{-1-3}$

$m_2=\frac{-6}{-4}$

$m_2=\frac{3}{2}$

Slope of AC, A= (4,4) and C=(-1,-1)

$m_3=\frac{-1-4}{-1-4}$

$m_3=\frac{-5}{-5}$

$m_3=1$

As $m_1\times m_3=-1\times 1=-1$

So, AB is perpendicular to AC.

Therefore, ABC form a right angle triangle.