Question

Find ratio in which point p(6,7) divides the segment joining a(8,9) and b(1,2) by section formula​

Answer 1

Given line AB and

• A(8,9)
• B(1,2)

point P divides the line AB in the ratio m:n

• P(6,7)

Thus by using section formula: (x = mx2+nx1/m+n) (y = my2 + ny1/m+n)

Thus for x:

• x = (mx2 + nx1)/(m+n)
• 6 = (m + 8n)/m+n
• 6m + 6n = m + 8n
• 6m - m = 8n - 6n
• 5m = 2n
• m/n = 2/5

Thus the ratio in which P divides line AB is m:n = 2:5

#answerwithquality

#BAL

Answer 2

The ratio in which the point P divides the given line segment AB is m:n=2:5

Step-by-step explanation:

Given line segment is  AB and also given that the points A(8,9) and B(1,2)

To find the ratio in which point P divides the given line segment AB :

• Let the ratio be m:n
• From the given the point P(6,7) divides the given line segment AB in the ratio m:n

By here using the section formula

($x=\frac{mx_2+nx_1}{m+n},y=\frac{my_2+ny_1}{m+n}$)

• Let $(x_1,y_1)$ be the point A(8,9) and
• Let $(x_2,y_2)$ be the point B(1,2) respectively
• Let (x,y) be the point P(6,7) respectively.

Now substitute the points in the section formula we get

• $x=\frac{mx_2 + nx_1}{m+n}$
• $6=\frac{m(1)+n(8)}{m+n}$
• $6=\frac{m+8n}{m+n}$
• $6(m+n)=m+8n$
• 6m+6n=m+8n
• 6m-m+8n-6n

• 5m=2n
• Therefore $\frac{m}{n}=\frac{2}{5}$

Therefore the ratio in which the point P divides the given line segment AB is m:n=2:5