Question

Without using Pythagoras theorem show that (12,8), (-2,6) and (6,0) are the vertices of right angled triangle.

Answer 1

Answer:

Just prove that slope b/w point A, B & B,C C, A & C, B is not same by straight line equation.

However you only need to prove that these line are not colinear.

Answer 2

The given vertices are right angled triangle, shown.

Step-by-step explanation:

Let  A (12, 8), B (- 2, 6) and C (6, 0) are the vertices of right angled triangle.

Using slope formula,

$\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$

The slope of AB = $\dfrac{6-8}{-2-12}$

= $\dfrac{-2}{-14}=\dfrac{1}{7}$

The slope of BC = $\dfrac{0-6}{6+2}$

= $\dfrac{-6}{8}=\dfrac{-3}{4}$

The slope of CA = $\dfrac{8-0}{12-6}$

= $\dfrac{8}{6}=\dfrac{4}{3}$

The slope of BC × The slope of CA

= $\dfrac{-3}{4}$ × $\dfrac{4}{3}$

= - 1

∴ BC ⊥ CA

Thus, the given vertices are right angled triangle, shown.