Question

In a classroom Chinni, Chameli and Nikki are seated at A(3, 1), B(6, 4) and C(8, 6)

respectively. Do you think they are seated in a same line? Give reasons for your

answer. ​

Answer 1

AnswEr:

If Chinni, Chameli & Nikki are seated at Points A,B & C. So, Points must be collinear.

AB + BC = AC

By Using Distance Formula We can Find AB, BC & AC.

$\rule{200}3$

$\dag\:\large\bold{\underline{\sf{For\:AB}}}$

A(3, 1) & B(6,4)

$\sf{Here}\begin{cases}\sf{x_1 \:=\: 3} \\ \sf{x_2\:=\: 6} \\ \sf{y_1\:=\; 1}\\ \sf{y_2\:=\: 4}\end{cases}$

$\longrightarrow\sf\: \sqrt{(x_2\:-\:x_1)^2\:+\:(y_2\:-\:y_1)^2}$

$\longrightarrow\sf\: \sqrt{(6 - 3)^2 + (4-1)^2}$

$\longrightarrow\sf\: \sqrt{(3)^2 + (3)^2}$

$\longrightarrow\sf\: \sqrt{9+9}$

$\longrightarrow\sf\: 3\sqrt{2}$

$\rule{200}3$

$\dag\:\large\bold{\underline{\sf{For\:BC}}}$

B(6,4) & C(8,6)

$\sf{Here}\begin{cases}\sf{x_1\:=\: 6}\\ \sf{y_1\:=\: 4} \\ \sf{x_2\:=\: 8} \\ \sf{y_2\:=\:6}\end{cases}$

$\longrightarrow\sf\: \sqrt{(8-6)^2 \:+\; (6-4)^2}$

$\longrightarrow\sf\: \sqrt{(4 + 4)}$

$\longrightarrow\sf\: 2\sqrt{2}$

$\rule{200}3$

$\dag\:\large\bold{\underline{\sf{For\:AC}}}$

A(3, 1) & C(8,6)

$\sf{Here}\begin{cases}\sf{x_1\:=\:3}\\ \sf{y_1\:=\:1}\\ \sf{x_2\:=\: 8} \\ \sf{y_2\:=\: 6}\end{cases}$

$\longrightarrow\sf\: \sqrt{(8-3)^2\:+\:(6-1)^2}$

$\longrightarrow\sf\: \sqrt{25\:+\:25}$

$\longrightarrow\sf\: 5\sqrt{2}$

Hence, AB = 3√2 , BC = 2√2 & AC = 5√2

$\longrightarrow\sf\: AB + BC = AC$

$\longrightarrow\sf\: 3\sqrt{2} \:+\: 2\sqrt{2}$

$\longrightarrow\sf\: 5\sqrt{2}$

Here, we can see that points are collinear.

So, that Chinni, Chameli & Nikki are seated in the same line.

Answer 2

Question :

In a classroom Chinni, Chameli and Nikki are seated at A(3, 1), B(6, 4) and C(8, 6)

respectively. Do you think they are seated in a same line? Give reasons for your answer.

Solution :

By Distance Formula :

$d \: = \sqrt{ ({x_{2} - x_{1})}^{2} + ({y_{2} - y_{1})}^{2}}$

AB = $3 \sqrt {2}$

BC = $2 \sqrt {2}$

AC = $5 \sqrt {2}$

Hence, A, B and C are seated in a straight line.