Answer:
P ≡ [tex](- \frac{5}{4}, \frac{15}{4})[/tex]
Step-by-step explanation:
The point P divides the line segment from A(-2,3) and B(1,6) in the ratio of 1 : 3.
So, AP : PB = 1 : 3.
Now, the coordinates of point P will be given by [tex](\frac{1 \times 1 + 3 \times (- 2)}{1 + 3}, \frac{1 \times 6 + 3 \times 3}{1 + 3})[/tex]
= [tex](- \frac{5}{4}, \frac{15}{4})[/tex] (Answer)
Note: Let there are two points with known coordinates [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] and another a point having coordinates (h,k) divides the line joining the two above points internally in the ratio m : n, then (h,k) is given by
(h,k) ≡ [tex](\frac{mx_{2} + nx_{1}}{m + n}, \frac{my_{2} + ny_{1}}{m + n})[/tex]
