Question

Solve the follow
(1) Find the ratio in which point P(k, 7) divides
the segment joining A (8,9) and B(1, 2). Also
find k.
Solution :​

Answer 1

Answer:

Question:-

Find the ratio in which point P( k , 7)

divides the segment joining A( 8,9 ) and B( 1,2 ) also find k.

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Required Answer:-

• Concept/Formula used:-

• Section Formula:-

x = mx2+nx1/m+n

y=my2+ny1/m+n

Section Formula is used when we have to find the ratio or value of m and n and also to find the value x and y co-ordinate if ratio m:n is provided in the question.

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Now,

by section Formula:-

y = my2 + ny1/ m+n

7 = m(9)+ n(2) / m+n

7 = 9m + 2n / m+n

7m + 7n = 9m + 2n

7m - 9m= 2n -7n

-2m = -2n

m/n = -2/-2

m/n = 1/1

x = mx2 + nx1 / m+n

k = (1)(8) + (1)(1) / 1 + 1

k = 8 + 1 /2

2k = 9

k = 9/2

k = 4.5

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verification for the value of k:-

put x=k=4.5

x = mx2+ nx1 / m+n

k = m(8) + n(1) / m+n

4.5 = 8m + n / m+n

4.5(m+n) = 8m + n

4.5m + 4.5n = 8m + n

4.5m - 8m = n - 4.5n

-3.5m = -3.5n

m/n = -3.5/-3.5

m/n = 1/1

-hence verified✅️

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hope it help you.