Math, asked by ashmit9588, 10 months ago

find the value of k for which the points A(9,K),B(4,-2)AND C(3,-3) are collinear..​

Answers

Answered by anandpagoti
9

Step-by-step explanation:

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Answered by Dhruv4886
0

The value of k = 3

Given:

A(9,K),B(4,-2) and C(3,-3) are collinear

To find:

The value of K

Solution:

Collinear points are those which are lies on same

Given that A(9,K),B(4,-2) and C(3,-3) are collinear  

The A, B and C are lies on same line

If we consider AB and BC as lines

⇒ slope of line AB = slope of line BC

As we know slope of line with points (x₁, y₁) and (x₂, y₂) is given by

m = (y₂-y₁) /(x₂-x₁)

Slope of line AB where A(9,K) and B(4,-2)

= (-2-k)/(4-9)

Slope of line BC where B(4,-2) and C(3,-3)

= (-3 + 2)/(3-4)    

As we know slope AB and BC will be equal

\frac{(-2-k) }{(4-9) } = \frac{(-3 + 2)}{(3-4) }  

⇒ (-2-k) (3-4) = (-3+2) (4-9)    

⇒ -6 + 8 -3k +4k = - 12 +27+8 -18        

⇒ K+ 2 = 5

⇒ K = 3    

The value of k = 3

#SPJ2

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