Question

Find the ratio in which the point (3, 1) divides the line joining the points (1, -1) and (4, 2).

Answer 1

Step-by-step explanation:

Using the section formula, if a point (x,y)divides the line joining the points (x1,y1)and (x2,y2) in the ratio m1:m2, then 

(x,y)=(m1+m2m1x2+m2x1,m1+m2m1y2+m2y1)

Given that ratio m1:m2=xy

points A(−5,−4) and B(−2,3) 

Let ratio be

m2m1=1m

Therefore, 

x=m1+m2m

Answer 2

Answer:

Ratio = 2:1

Step-by-step explanation:

We know,

Section Formula = P(x,y) = $(\frac{mx_{2}+nx_{1}}{m+n} ,\frac{my_{2}+ny_{1}}{m+n} )$

where, P(x,y) = (3,1) ; A$(x_{1},y_{1})$=(1,-1) ; B$(x_{2},y_{2})$=(4,2)

Let us consider the ratio as k:1

=>(3,1) = $(\frac{4k+1}{k+1} , \frac{2k-1}{k+1} )$

On comparing the coordinates ,

=> 3 = $\frac{4k+1}{k+1}$

=> 3(k+1) = 4k+1

=>3k+3 = 4k+1

=> 3 -1 = 4k -3k

=> k = 2

Therefore the ratio is 2:1   .

Note:

You can also compare the y-coordinates you'll get the same answer.

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