Question

Find the ratio in which point p(6, 7) divides the segment joining A(8, 9) and B(1, 2) by completing the following activity.

Answer 1

Answer:

The ratio in which the point p divide the line segment AB is     2 : 5

Step-by-step explanation:

Given as :

The point = p = x , y = (6 , 7)

The point of line segment AB , A = $x_1 , y_1$ = (8 , 9)

and B = $x_2 , y_2$ =  (1, 2)

Let the ration in which line segment AB is divided = m : n

According to question

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

Or, 6 = $\dfrac{1 m + 8 n}{m + n}$

Or, 6 m + 6 n = m + 8 n

Or, 6 m - m = 8 n - 6 n

Or, 5 m = 2 n

Or, 5 m - 2 n = 0            ...........A

Again

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

Or, 7 = $\dfrac{2 m + 9 n}{m + n}$

Or, 7 m + 7 n = 2 m + 9 n

Or, 7 m - 2 m = 9 n - 7 n

Or, 5 m = 2 n

Or, 5 m - 2 n = 0             ........B

Solving eq A and eq B

5 m - 2 n = 0

i.e 5 m = 2 n

Or, m : n = 2 : 5

So, The ratio in which the point p divide the line segment = 2 : 5

Hence, The ratio in which the point p divide the line segment AB is 2 : 5 Answer