Question

find the ratio in which the point 4 8 ride the line segment joining the points 5 7 and 39​

Answer 1

Answer:

1 : 1

Step-by-step explanation:

Correct Question :-

Find the ratio in which the point P(4 , 8) divide the line segment joining the points Q(5 , 7) and R(3 , 9).

Given,

P = (4 , 8)

Q = (5 , 7)

R = (3 , 9)

To Find :-

The ratio that the point 'P' divides the line segment QR.

How To Do :-

We need to find the ratio by substituting the value of co-ordinates in the section(internal formula). After that we need to equate both 'x' terms and 'y' terms we can see that we will get the ratio same in both cases.

Formula Required :-

Section (Internal Division) formula :-

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

Solution :-

Let, the ratio be 'm : n'

P = (4 , 8)

→ x = 4 , y = 8

Q = (5 , 7)

→ x_1 = 5 , y_1 = 7

R = (3 , 9)

→ x_2 = 3 , y_2 = 9

Substituting in the formula :-

$(4,8)=\left(\dfrac{m(3)+n(5)}{m+n},\dfrac{m(9)+n(7)}{m+n}\right)$

$(4,8)=\left(\dfrac{3m+5n}{m+n},\dfrac{9m+7n}{m+n}\right)$

Equating both 'x' terms and 'y' terms :-

First equating 'x' terms :-

4 = 3m + 5n/ m + n

4(m + n) = 3m + 5n

4m + 4n = 3m + 5n

4m - 3m = 5n - 4n

m = n

m/n = 1

m : n = 1 : 1

Equating the 'y' terms :-

8 = 9m + 7n/m + n

8(m + n) = 9m + 7n

8m + 8n = 9m + 7n

8m - 9m = 7n - 8n

-m = -n

m = n

m/n = 1

m : n = 1 : 1

Since, we can say that both ratios are same.

∴m : n = 1 : 1