Question

Check whether the points (1,2),(-3,5) and (1,6)are collinear

Answer 1

Answer:

Given coordinates are not collinear.

Step-by-step explanation:

Inorder to check whether the given coordinates are collinear or not, we must know the concepts to find collinearity.

Two common methods are:-

• Area of triangle - If area of triangle formed by the given coordinates is 0, this implies that the coordinates are collinear.
• Concept of Slope - If the slope of the pair of any two coordinate is same this implies that the coordinates are collinear.

We will use the method of area of triangle.

Area of triangle is given by below formula:

$\boxed{\sf\Delta = \dfrac{1}{2} \left|x_1 (y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)\right|}$

Let's assume the given coordinates as,

• (x1, y1) = (1, 2)
• (x2, y2) = (-3, 5)
• (x3, y3) = (1, 6)

So area is given by,

$\sf\Delta = \dfrac{1}{2} \left | x_1 (y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)\right |$

$\sf\Delta = \dfrac{1}{2} \left| 1(5- 6) - 3(6 - 2) + 1(2 - 5)\right|$

$\sf\Delta = \dfrac{1}{2} \left |1 ( - 1) - 3(4) + 1( - 3)\right|$

$\sf\Delta = \dfrac{1}{2} \left | - 1 - 12 - 3\right|$

$\sf\Delta = \dfrac{1}{2}(15)$

$\sf\Delta = 7.5 \: sq \: units$

This is not 0, therefore the given coordinates are not collinear.