Question

(1) Find the ratio in which point P(6, 7) divides the segment joining A(89) and B(1,2) by completing the following activity, ​

Answer 1

$\huge\fbox\green{Answer}$

Let the ration in which line segment AB is divided = m : n

According to question

x =

$\dfrac{m x_2 + n x_1}{m + n}$

m+n

mx

2

+nx

1

Or, 6 =

$\dfrac{1 m + 8 n}{m + n}$

m+n

1m+8n

Or, 6 m + 6 n = m + 8 n

Or, 6 m - m = 8 n - 6 n

Or, 5 m = 2 n

Or, 5 m - 2 n = 0 _____A

Again

y =

$\dfrac{m y_2 + n y_1}{m + n}$

m+n

my

2

+ny

1

Or,

$7 = \dfrac{2 m + 9 n}{m + n}$

m+n

2m+9n

Or, 7 m + 7 n = 2 m + 9 n

Or, 7 m - 2 m = 9 n - 7 n

Or, 5 m = 2 n

Or, 5 m - 2 n = 0 .______B

Solving eq A and eq B

5 m - 2 n = 0

i.e 5 m = 2 n

Or, m : n = 2 : 5

So, The ratio in which the point p divide the line segment = 2 : 5

Hence, The ratio in which the point p divide the line segment AB is 2 : 5 Answer

Answer 2

Answer:

Let the ration in which line segment AB is divided = m : n

According to question

x =

\dfrac{m x_2 + n x_1}{m + n}

m+n

mx

2

+nx

1

m+n

mx

2

+nx

1

Or, 6 =

\dfrac{1 m + 8 n}{m + n}

m+n

1m+8n

m+n

1m+8n

Or, 6 m + 6 n = m + 8 n

Or, 6 m - m = 8 n - 6 n

Or, 5 m = 2 n

Or, 5 m - 2 n = 0 _____A

Again

y =

\dfrac{m y_2 + n y_1}{m + n}

m+n

my

2

+ny

1

m+n

my

2

+ny

1

Or,

7 = \dfrac{2 m + 9 n}{m + n}7=

m+n

2m+9n

m+n

2m+9n

Or, 7 m + 7 n = 2 m + 9 n

Or, 7 m - 2 m = 9 n - 7 n

Or, 5 m = 2 n

Or, 5 m - 2 n = 0 .______B

Solving eq A and eq B

5 m - 2 n = 0

i.e 5 m = 2 n

Or, m : n = 2 : 5

So, The ratio in which the point p divide the line segment = 2 : 5

Hence, The ratio in which the point p divide the line segment AB is 2 : 5 Answer