Question

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Answer 1

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Answer 2

❏ Question:-

Find the value of y if the points A(3,4) , B(6,y) and C(7,8) are collinear .

❏ Solution:-

We know that the points A(3,4) , B(6,y) and C(7,8) will be collinear if the area enclosed by these points is Zero ( or 0).

Now we know that area enclosed by the points

$\sf (x_1,y_1)\:,\:(x_2,y_2)\:,\:(x_3,y_3)$

is given by the formula,

$\sf\implies A=\dfrac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]$

Now, from the given points area enclosed by them is ,

$\sf\implies A=\dfrac{1}{2}[3(y-8)+6(8-4)+7(4-y)]=0$

$\sf\implies \dfrac{1}{2}[3y-\cancel{24}+\cancel{24}+28-7y]=0$

$\sf\implies \dfrac{1}{2}[-4y+28]=0$

$\sf\implies [-4y+28]=0$

$\sf\implies 4y=28$

$\sf\implies y=\dfrac{\cancel{28}}{\cancel4}$

$\sf\implies\boxed{ \large{\red{y=7}}}$