Question

Find the value of k such that L(3,-1) M(0,5) N(k,-4)

Answer 1

Complete the question !

Answer 2

sorry, Find the value of k such that L(3,-1) M(0,5) N(k,-4) are collinear

Answer 3

The points L , M and N are collinear if :
\[\Large \overrightarrow {LM}=\alpha\Large \overrightarrow {LN}\]
So :
\[\Large\begin{pmatrix}0-3\\5-(-1)\end{pmatrix}=\alpha\begin{pmatrix}k-3\\-4-(-1)\end{pmatrix}\]
So :
\[\Large\begin{cases}\alpha(k-3)=-3\\-3\alpha=6\end{cases}\]
From the 2nd equation we get :
\[\Large \alpha=-2\]
And from the 1st we get :
\[\Large -2(k-3)=-3\]
so :
\[\Large k-3=\frac32\]
so :
\[\Large k=\frac32+3=\frac 92\]

Answer 4

i don't know how to use alpha

Answer 5

substitute ... alpha ....

Answer 6

From the 2nd equation we get the value of alpha, then we replace the value of alpha in the 1st equation

Answer 7

ok, thanks.