Answer with explanation:
It is given that ,Point P partitions the directed segment from A to B into a 1:3 ratio. Q partitions the directed segment from B to A into a 1:3 ratio.
Let coordinates of A be (a,0) and B be (0,b).
And Coordinate of Point P be (x,y) and coordinate of Q be (p,q).
We will use section formula to determine whether P and Q are the same point or not.
Formula for external Division
[tex]x=\frac{m x_{2}+n x_{1}}{m+n}\\\\y=\frac{my_{2}+n y_{1}}{m+n}\\\\x=\frac{1\times 0+3\times a}{1+3}\\\\x=\frac{3a}{4}\\\\y=\frac{1\times b+3\times 0}{1+3}\\\\y=\frac{b}{4}\\\\p=\frac{1\times a+3\times 0}{1+3}\\\\p=\frac{a}{4}\\\\q=\frac{1\times 0+3\times b}{1+3}\\\\x=\frac{3 b}{4} [/tex]
Coordinates of P and Q are
[tex]=P(\frac{a}{4},\frac{3b}{4}),Q(\frac{3b}{4},\frac{a}{4})[/tex]
So, P and Q are not the same point.
Option D: No, P is closer to A , and Q is closer from B .
