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

1.	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» 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.