Question

Given A , B and C are collinearAB : AC = 2/5A = ( -3 , 6 )B = ( n , q )C = ( -3 , -4 )What are the values of n and q and The ordered pair of B ?

Answer 1

Given A , B and C are collinear

AB : AC = 2/5

A = ( -3 , 6 )

B = ( n , q )

C = ( -3 , -4 )

Note : the x coordinates of A = x-coordinates of C = -3

As the three points are collinear

So, the x-coordinates of the point B = -3

so, n = -3

Now, we will find the y-coordinates of the point B

AB : AC = 2/5

So,

`\begin{gathered} (ya-yb)/(ya-yc)=(2)/(5) \\ (6-q)/(6-(-4))=(2)/(5) \\ (6-q)/(10)=(2)/(5) \\ 5(6-q)=20 \\ 6-q=4 \\ q=6-4 \\ q=2 \end{gathered}`

so, the y-coordinates of the point B = q = 2

so, n = -3 and q = 2

The ordered pair of B is ( -3 , 2 )