Question

If the points (2,3)(-1,k) and (5,8) are collinear then k =​

Answer 1

Answer:

Answer

If three points are collinear, then the slope of the line joining the first two points is equal to that of the last two.

Apply the slope formula

(x2−x1).

(y2−y1)

If collinear then

2+2

−2+5

=

6

a+2

2

9

=a+2

a=

2

5

Answer 2

Given : The three collinear points are (2,3) , (-1,k) and (5,8)

To find : The value of k

Solution :

The value of k is -2

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to find the value of k, by using the available data)

If three points are collinear then the area of the triangle formed by those three points (taken as vertices) , will be zero.

Here,

(x1,y1) = (2,3)

(x2,y2) = (-1,k)

(x3,y3) = (5,8)

Area of the formed triangle by the given three points :

= ½ [x1(y2-y3) + x2(y3-y1) + x3(y1-y2)]

= ½ [2(k-8) - 1(8-3) + 5(3-k)]

= ½ × (2k-16-5+15-5k)

= [½ × (-3k-6)] sq.unit

According to the previously mentioned principle about collinear points, we get :

½ × (-3k-6) = 0

-3k-6 = 0

-3k = 6

k = -2

(This will be considered as the final result.)

Hence, the value of k is -2