Question

Using the formula, show that the points A(7,-5),B(9,-3) and C(13,1) ate collinear

Answer 1

Solution :-

We need to show that the points A ( 7 , -5 ), B ( 9 , -3 ) and C ( 13 , 1 ) are collinear.

The given points are said to be collinear if the area of triangle ABC is zero.

$\boxed{\bf Area \ of \ triangle = \dfrac{1}{2} \times [ \ x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)}$

Here :-

$\bullet \sf \ x_1= 7 \ , \ y_1 = -5 \\\\\bullet \ x_2 = 9 \ , \ y_2 = -3 \\\\\bullet \ x_3 = 13 \ , \ y_3 = 1$

$\longrightarrow \sf \dfrac{1}{2} \times [ \ 7( -3-1)+9(1-(-5))+13(-5-(-3)) \ ] \\\\\longrightarrow \dfrac{1}{2} \times [ \ 7 ( -3-1)+9(1+5)+13(-5+3) \ ] \\\\\longrightarrow \dfrac{1}{2} \times [ \ (7 \times -4 )+( 9 \times 6 ) + (13 \times -2 ) \ ] \\\\\longrightarrow \dfrac{1}{2} \times [ \ -28+54-26 \ ] \\\\\longrightarrow \dfrac{1}{2} \times [ \ 26-26 \ ] \\\\\longrightarrow \dfrac{1}{2} \times 0 \\\\\longrightarrow 0$

∴ The given points are collinear.

Answer 2

Step-by-step explanation:

Given :

• that the points A(7,-5),B(9,-3) and C(13,1

To Find :

• Find the collinear

Solution :

= 1/2[ 7(- 3 - 1 ) + 9 (1 + 5 ) + 13 (- 5 + 3) ]

= 1/2[ 7 × - 4 + 9 × 6 + 13 × - 2]

= 1/2( - 28 + 54 - 26)

= 1/2(54 - 54)

= 0/2

= 0