find the value of k for which the points A(9,K),B(4,-2)AND C(3,-3) are collinear..
Answers
Step-by-step explanation:
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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
⇒
⇒ (-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
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