Math, asked by ghoshutpal001, 10 months ago

Find the value of k if the point s)p(5,4),q(7,k) and r(9,-2)are collinear

Answers

Answered by CRAZYMIND

Answer:

Step-by-step explanation:

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Answered by virtuematane

Answer:

Hence, the value of k such that the points p(5,4),q(7,k) and r(9,-2) are collinear is:

k=1

Step-by-step explanation:

If three points $(x_1, y_1),(x_2, y_2)$ and $(x_3, y_3)$ are collinear then $[x_1(y_2 - y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]=0$

Hence here we have:

$(x_1,y_1)=p(5,4)$

$(x_2,y_2)=q(7,k)$

$(x_3,y_3)=r(9,-2)$

Since, it is given that the points are collinear hence,

$5(k+2)+7(-2-4)+9(4-k)=0\\\\\5k+10-14-28+36-9k=0\\\\-4k+4=0\\\\4k=4\\\\k=1$

Hence, the value of k such that the points p(5,4),q(7,k) and r(9,-2) are collinear is:

k=1

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