Question

The points (2,3) divides the line joining(1,2) and (5,6) in the ratio

Answer 1

Answer:

1:3

Explanation:

Let P(2,3) divide the line joining A(1,2) and B(5,6) in the ratio k:1

Using section formula and comparing the values of the x-coordinate:

2= kx2+x1/k+1

2= 5x2+1/k+1

2(k+1)=5k+1

=2k+2=5k+1

=2-1=5k-2k

=1=3k

=k=1/3

1/3:1

=1:3

There's your answer

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Answer 2

Answer:

1:3

Explanation:

Given that , point ( 2,3) divides the line joining (1,2) and (5,6) in the ratio.

To find the ratio.

So,

Let the point (2,3) divides the line joining (1,2) and (5,6) in the ratio K:1

By using the section formula,

$x = (\frac{Kx2~+~x1}{K~+~1})~~~~and ~~y=(\frac{Ky2~+~y1}{K~+~1})$

where x = 2 and y = 3  of the point (2,3)

$2=(\frac{5K~+~1}{K~+~1} ) ~~~~and~~~3=(\frac{6K~+~2}{K~+~1})$

$5K~+~1=2K~+~2 ~~~and~~~6K~+~2=3K~+~3$

$3K=1~~~and~~3K=1$

$K=1:3$

Therefore the point (2,3) divides the line joining the point (1,2) and (5,6) in ratio 1:3

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