Answer: The co-ordinates of point B are (4, -5).
Step-by-step explanation: We are given to find the co-ordinates of point B in the diagram.
From the diagram, we note that
the co-ordinates of point A and C are (1, 5) and (1.75, 2.5) respectively.
Also, the point C divides the line segment AB internally in the ratio 1 : 3.
We know that if a point P divides a line segment joining the points (a, b) and (c, d) internally in the ratio m : n, then the co-ordinates of the point P are
[tex]P=\left(\dfrac{mc+na}{m+n},\dfrac{md+nb}{m+n}\right).[/tex]
Here, (a, b) = (1, 5), m : n = 1 : 3 and (c, d) = ?
Therefore, the co-ordinates of point C will be
[tex]C=\left(\dfrac{1\times c+3\times1}{1+3},\dfrac{1\times d+3\times5}{1+3}\right)\\\\\\\Rightarrow (1.75,2.5)=\left(\dfrac{c+3}{4},\dfrac{d+15}{4}\right)\\\\\\\Rightarrow 1.75=\dfrac{c+3}{4},~~~~~2.5=\dfrac{d+15}{4}\\\\\\\Rightarrow c+3=7,~~~~~~~~\Rightarrow d+15=10\\\\\\\Rightarrow c=4,~~~~~~~~~~~~~\Rightarrow d=-5.[/tex]
Thus, the co-ordinates of point B are (4, -5).
