Question

if the point A(-2,3) B(1,2) and C(k,0) are collinear, then k​

Answer 1

Answer:

Step-by-step explanation:

applying slope1=slope2

you get answer

-1/3= -2/k-1

1/3=2/k-1

6=k-1

k=7

Answer 2

ANSWER:-

Given:

⚫A(-2,3)

⚫B(1,2)

⚫C(k,0)

are collinear.

To find:

The value of k.

Solution:

Let the given points be A(-2,3), B(1,2),C(k,0).

•The above points are collinear, they will lie on the same line.

Area of ∆ABC= 0.

The formulas:

$= > \frac{1}{2} [x1(y2 - y1) + x2(y3 - y1) + x3(y1 - y2)]= 0$

Here,

•x1 = -2, y1=3

•x2 = 1, y2= 2

•x3 = k, y3= 0

Putting value of the above formulas:

$= > \frac{1}{2} [- 2(2 - 0) + 1(0 - 3) + k(3 - 2)]= 0 \\ \\ = > \frac{1}{2} [- 2(2) + 1( - 3) + k(1)]= 0 \\ \\ = > \frac{1}{2} [- 4 + ( - 3) + k]= 0 \\ \\ = > \frac{1}{2} ( - 4 - 3 + k) = 0 \\ \\ = > \frac{1}{2} ( - 7 + k) = 0 \\ \\ = > \frac{ - 7 + k}{2} = 0 \\ \\ = > - 7 + k = 0 \\ \\ = > k = 0 + 7 \\ \\ = > k = 7$

Thus,

The value of k is 7.

Thank you.