Without using Pythagoras theorem, show that points A (4, 4), B (3, 5)

1.	Without using Pythagoras theorem, show that points A (4, 4), B (3, 5) and C (- 1, – 1) are the vertices of a right-angled triangle.
Answer» Given, A(4,4), B(3, 5), C (-1, -1). Slope of AB = \(\frac {y_2-y_1}{x_2-x_1}= \frac {5-4}{3-4} = -1\) Slope of BC = \(\frac {-1-5}{-1-3}= \frac {-6}{-4}\) = 3/2 Slope of AC = \(\frac {-1-4}{-1-4}=1\) Slope of AB x slope of AC = – 1 x 1 = – 1 ∴ side AB ⊥ side AC ∴ ∆ABC is a right angled triangle right angled at A. ∴ The given points are the vertices of a right angled triangle.

Without using Pythagoras theorem, show that points A (4, 4), B (3, 5) and C (- 1, – 1) are the vertices of a right-angled triangle.

Answer»

Given, A(4,4), B(3, 5), C (-1, -1).

Slope of AB = \(\frac {y_2-y_1}{x_2-x_1}= \frac {5-4}{3-4} = -1\)

Slope of BC = \(\frac {-1-5}{-1-3}= \frac {-6}{-4}\) = 3/2

Slope of AC = \(\frac {-1-4}{-1-4}=1\)

Slope of AB x slope of AC = – 1 x 1 = – 1

∴ side AB ⊥ side AC

∴ ∆ABC is a right angled triangle right angled at A.

∴ The given points are the vertices of a right angled triangle.