Question

What is value of k if the points (2,-3),(k,-1) and(0,4) is collinear

Answer 1

Answer:

answer will be 2 for the k

Answer 2

Solution

Given :-

The points (2, -3) , (k, -1) and (0, 4) are collinear .

Find :-

Value of k

Explanation

Let,

Given point be A(2,-3) , B(k,-1) , C(0,4)

Condition For Collinear,

slopes of any two pairs of points will be equal.

Formula Of Slope

★ Slope(any two point) = (y - y')/(x - x')

Where,

(x,y) & (x' , y') be any point.

Now, Calculate Slope of AB

Where,

A(2,-3) , B(k,-1) ,

➡AB = (-1+3)/(k-2)

➡AB = 2/(k+2)

Now, Calculate Slope of BC

where ,

B(k,-1) , C(0,4)

➡BC = (4+1)/(0-k)

➡BC = 5/k

According to condition,

AB = BC

We get,

➡ 2/(k+2) = 5/k

➡2k = 5*(k+2)

➡2k = 5k + 10

➡5k - 2k = -10

➡3k = -10

➡k = -10/3

Hence

Value of k = -10/3

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