Question

Find the value of y if A(-2,2) , B (2,y) , C (3,7) are collinear?

Answer 1

Question -

Find the value of y if A(-2,2),B(2,y), C(3,7) are collinear?

Solution -

Given points are A(-2,2) , B(2,y),C(3,7)

Let,

$(x _{1} ,y_1)=( - 2,2),(x_2,y_2)=(2,y) \: \: and \: \: (x_3,y_3)=(3,7)</p><p></p><p></p><p></p><p>$

Now,

$x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) = 0$

Putting the values we will get -

$- 2(y - 7) + 2(7 - 2) + 3(2 - y) = 0$

$- 2y + 14 + 2 \times 5 + 6 - 3y = 0$

$- 2y + 14 + 10 + 6 - 3y = 0$

$- 5y + 30 = 0$

$- 5y = - 30$

$y = \frac{ - 30}{ - 5}$

$y = 6$

Therefore the value of y is 6