Question

If the points $A(x,2),B(-3,-4)$ and $C(7,-5)$ are collinear, then the value of $x$ is :

• A. $-63$
• B. $63$
• C. $60$
• D. $-60$

Answer 1

The correct option is A $-63$

Given points are $A(x,2)B(-3,-4)C(7,-5)$

$(x_1,y_1)=(x,2),(x_2,y_2)=(-3,-4)(x_3,y_3)=(7,-5)$

$x_1[y_2-y_3]+x_2[y_3-y_1]+x_3[y_1-y_2]=0$

$x\left[\right(-4)-(-5\left)\right]+(-3)\left[\right(-5)-2]+7[2-(-4\left)\right]=0$

$x(-4+5)-3(-5-2)+7(2+4)=0$

$x\left(1\right)-3(-7)+7\left(6\right)=0$

$x+21+42=0$

$x+63=0$

$x=-63$

$\therefore$ The value of x is $-63$.