Question

Find the ratio in which (4, 5) divides the join of (2, 3) and (7. 8).
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Answer 1

Step-by-step explanation:

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

Applying the formula,

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

→ 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.