Question

Point A is located at (3,6) and point B is located at (10, -2) What are the coordinates of the point that partitions the directed line segment AB in a 1:3 ratio?​

Answer 1

Answer:

The coordinates of point P is $(\frac{19}{4} ,4)$

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:

$(a,b) = (\frac{m_2x_1 + m_1x_2}{m_1+m_2}, \frac{m_2y_1 + m_1y_2}{m_1+m_2})$

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:

$(a,b) = (\frac{3(3) + 1(10)}{1+3}, \frac{3(6) + 1(-2)}{1+3})\\\implies (a,b)= (\frac{9+10}{4} , \frac{18-2}{4}) =(\frac{19}{4} ,\frac{16}{4} )\\\implies (a,b) = (\frac{19}{4} ,4 )$

Hence, the coordinates of point P is $(\frac{19}{4} ,4)$