Answer:
The coordinates of point P is [tex](\frac{19}{4} ,4)[/tex]
Step-by-step explanation:
Here, the coordinates of the point A and B are given as:
A (3,6) and B(10,-2)
Let us assume the point P (a,b) divides the line segment AB in ratio 1:3.
Now, by SECTION FORMULA:
The coordinate of the point (a,b) which divides the line segment with points (x1,y1) and (x2,y2) in ratio m1 : m2 is given as:
[tex](a,b) = (\frac{m_2x_1 + m_1x_2}{m_1+m_2}, \frac{m_2y_1 + m_1y_2}{m_1+m_2})[/tex]
Now, here putting the values of the points A and B as (3,6) and (10,-2) adn ratio m1 : m2 as 1:3, we get:
[tex](a,b) = (\frac{3(3) + 1(10)}{1+3}, \frac{3(6) + 1(-2)}{1+3})\\\implies (a,b)= (\frac{9+10}{4} , \frac{18-2}{4}) =(\frac{19}{4} ,\frac{16}{4} )\\\implies (a,b) = (\frac{19}{4} ,4 )[/tex]
Hence, the coordinates of point P is [tex](\frac{19}{4} ,4)[/tex]
