Question

Verify whether the points (-2,3),(4,2) and (10,1) are called colliner or not?​

Answer 1

If they are collinear they must have same slope(or you can say, they lie on the same line).

Slope of (-2, 3) and (4,2)= (y₂ - y₁)/(x₂ - x₁)

              ⇒ (3 - 2)/(-2 - 4)

              ⇒ - 1/6

Slope of (-2, 3) and (10,1)= (y₂ - y₁)/(x₂ - x₁)

              ⇒ (3 - 1)/(- 2 - 10)

              ⇒ 2/(-12)

              ⇒ - 1/6

As both are same, they are collinear.

Answer 2

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°•° We know that ,

• A line that passes through the same points / lines forming a distinct slope , it is known as co-linear.

Here , from given data :

Let ,

ㅤㅤㅤ➪ $\boxed{\sf{\red{y_1 \:=\: 1}}}$

ㅤㅤㅤ➪ $\boxed{\sf{\red{y_2 \:=\: 2}}}$

ㅤㅤㅤ➪ $\boxed{\sf{\red{y_3 \:=\: 3}}}$

• Again ,

ㅤㅤㅤ➪ $\boxed{\sf{\blue{x_1 \:=\: ( - 2 )}}}$

ㅤㅤㅤ➪ $\boxed{\sf{\blue{x_2 \:=\: 4 }}}$

ㅤㅤㅤ➪ $\boxed{\sf{\blue{x_3 \:=\: 10 }}}$

Now ,

• First slope : ( -2 , 3 ) & ( 4 , 2 )

ㅤㅤㅤ➪ $\bf{\dfrac{y_2 - y_1}{ x_2 - x_1 }}$

ㅤㅤㅤ➪ $\bf{\dfrac{ 2 - 1 }{ 4 - ( -2 ) }}$

ㅤㅤㅤ➪ $\bf{\dfrac{1}{ 4 + 2 }}$

ㅤㅤㅤ➪ $\bf{\dfrac{1}{6}}$ ( 6 , 1 )

• Second slope : ( 4 , 2 ) & ( 10 , 1 )

ㅤㅤㅤ➪ $\bf{\dfrac{ y_3 - y_2 }{ x_3 - x_2 }}$

ㅤㅤㅤ➪ $\bf{\dfrac{ 3 - 2 }{ 10 - 4 }}$

ㅤㅤㅤ➪ $\bf{\dfrac{1}{6}}$ ( 6 , 1 )

As both the result are same

•°• the slopes are co-linear...

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