Question

Point P lies on the directed line segment from A(2,3) to B(8,0) and ​partitions the segment in the ratio 22 to 11. ​ ​What are the coordinates of ​point P ?

Answer 1

Answer:

The coordinates of point P is 6 , 1

Step-by-step explanation:

Given as :

The point P lies on directed line segment from points A and B

A = ( $x_1$ ,  $y_1$ ) = (2 ,3)

B = ( $x_2$ ,  $y_2$  ) =  (8 , 0)

The partitions segments in the ratio = m : n = 22 : 11

Let the coordinate of point P = x , y

Now, According to question

x = $\dfrac{m\times x_2 + n\times x_1}{m + n}$

y = $\dfrac{m\times y_2 + n\times y_1}{m + n}$

Now

x = $\dfrac{m\times x_2 + n\times x_1}{m + n}$

Or, x = $\dfrac{22\times 8 + 11\times 2}{22 + 11}$

Or, x =  $\dfrac{176 + 22}{33}$

Or, x = $\dfrac{198}{33}$

∴ x = 6

Again

y = $\dfrac{m\times y_2 + n\times y_1}{m + n}$

Or, y = $\dfrac{22\times 0 + 11\times 3}{22 + 11}$

Or, y =  $\dfrac{0 + 33}{33}$

Or, y = $\dfrac{33}{33}$

∴ y = 1

So, The coordinates of point P = x , y = 6 , 1

Hence, The coordinates of point P is 6 , 1  Answer