Question

Line segment 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 :

( 20/3 , 4 )

Given :

• AB Line segment.
• Point A( 9 , 3 ) and B( 2 , 6 )
• AB divided into 1 : 2.

Solution :

We have,( Section formula )

$\tt\dagger \: \: \:x = \frac{m_1 x_2 + m_2 x_1 }{m_1 + m_2}$

$\tt\dagger \: \: \: y =\frac{m_1 y_2 + m_2 y_1 }{m_1 + m_2}$

Here,

• m1 = 1.
• m2 = 2.
• x1 = 9.
• x2 = 2.
• y1 = 3.
• y2 = 6.

Now,

For X,

$\tt \longmapsto \frac{1(2) + 2(9)}{3}$

$\tt \longmapsto \frac{20}{3}$

$\rule{90}1$

For Y,

$\tt \longmapsto \frac{1(6) + 2(3)}{3}$

$\tt \longmapsto \frac{12}{3}$

$\tt \longmapsto 3.$

So,

Our Coordinate become be ( x , y )( 20/3 , 4 )

Therefore, the coordinate of point that line segment dividend in 1 : 2 is ( 20/3 , 4 )

$\rule{200}3$

Note : Graph provide above.