Question

line segments AB has endpoints A(9,3) and B(2,6). Find the coordinates of the point that divides the line segment directed from A to B in the ratio of 1:2.

Answer 1

Answer:

The coordinates of the point that divides the line segment in the ratio of 1:2 is (x,y)  =  (20/3 , 4)

Step-by-step explanation:

The end point coordinates of the  segment AB is A(9,3) and B(2,6)

Let us assume the point P(x,y) divides the segment AB in the ratio 1: 2

⇒AP : PB  = 1: 2

Now, by SECTION FORMULA:

If The point (x,y) divides the line segment with points (x1,y1) and (x2,y2) in the ratio m1: m2, then the coordinates of (x,y) is given as:

$(x,y) = ({\frac{x_2 m_1 + m_2 x_1}{m1 + m2} , \frac{y_2 m_1 + m_2 y_1}{m1 + m2} })$

Applying the section formula in the given cindition,

here m1 :m2   = 1 :2

we get, $(x,y) = ({\frac{2(1) + 2(9) }{1 +2} , \frac{6(1) + 2(3)}{1 + 2} })\\\implies (x,y) = (\frac{2 + 18}{3} ,\frac{6 + 6}{3})\\ \implies (x,y) = (\frac{20}{3}, \frac{12}{3} )$

Now, comparing each ordinate separately

$x = \frac{20}{3} ,y = \frac{12}{3} = 4$

⇒ The coordinates of P(x,y)  =  (20/3 , 4)

Hence, the coordinates of the point that divides the line segment in the ratio of 1:2 is (x,y)  =  (20/3 , 4)