Question

2. Determine whether the given set of points in each case are collinear or not.
(i) (7,–2),(5,1),(3,4)

Answer 1

Answer:

Yes, given points are collinear.

Step-by-step explanation:

Let the points (7 -2), (5, 1) and (3, 4) be A, B and C respectively.

and Let these points be the vertices of a $\Delta ABC$.

Now, we find the area of triangle.

If area of triangle is zero, then the given points are collinear otherwise not.

Area of triangle = $\cfrac{1}{2}\left[ x_1(y_2 - y_3) + x_2(y_3 - y_1 ) + x_3(y_1-y_2) \right]$

So, $x_1 = 7, x_2 = 5, x_3 = 3, y_1 = -2, y_2 = 1 \text{ and } y_3 = 4.$

$\text{ar }(\Delta ABC) = \cfrac{1}{2}\left[ (7)(1-4) + 5(4-(-2)) + 3(-2-1) \right]$

$=\cfrac{1}{2} \left[ 7(-3)+5(4+2)+3(-3)\right]$

$=\cfrac{1}{2}\left[ -21 + 5\times 6 -9\right]$

$=\cfrac{1}{2}\left[ -30+30\right]$

$=\cfrac{1}{2}\times 0$

$=0$

$\text{Since, ar}(\Delta ABC) = 0$

$\text{Thus, given points are collinear.}$

Please mark my answer as BRAINLIEST.