calculate the value of P is the points A(6;5), B(3;2) and C (2p;p+4) are co-linnear

Question

Also honestly have no clue whatsoever. I have tried jotting down a graph and just finding the differences between A and B and minusing them from B to create C. I know this is completely wrong! Please help :)

Answer 1

We know that all of the points lie on the same line; call it $L$. We can use the first two points to find the slope of $L$, which we call $m$.

$$ m=\frac{2-5}{3-6}=\frac{-3}{-3}=1. $$

Now, we can write out an equation for $L$: $y=mx+b=x+b$ To find $b$, we plug in the point $A$: $5=6+b\implies b=-1$. Thus, the equation for $L$ is $y=x-1$. Now, we plug the point $C$ into this and solve for $p$:

$$ p+4=2p-1\implies p=5. $$