Question

find the ratio in which line segement joining point (2,3) (7,8) is divided by (4,5)​

Answer 1

Answer:

Let the point P (4,5) divides the segment A(2,3) and (7,8) in the ratio of k:1.

The Division formula , i.e if a point P(x,y) divides (a,b) and (c,d) in m:n, then

x = \frac{mc+na}{m+n}

m+n

mc+na

and y = \frac{md+nb}{m+n}

m+n

md+nb

Applying the formula,

4= \frac{7 k +2}{k+1}4=

k+1

7k+2

→ 4(k +1)= 7 k+ 2

→ 4 k +4 =7 k +2

→ 7 k - 4 k= 4-2

→ 3 k = 2

→ k =2/3

So, (4,5) divides the join of (2,3) and (7,8) in the ratio of 2:3.

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