Question

If point (4, 3) divides the join of (x, 3) are (5, -4) in the ratio of 1:2 then the value of x is

Answer 1

Answer:

Step-by-step explanation:

(5,-4) & (x,3) are divided in the ratio 1:2 by the point (4,3)

Here; $x$= 4

         $y$= 3

         $x_{1}$= 5

         $x_{2}$= x

         $y_{1}$= -4

         $y_{2}$= 3

         $m$= 1

         $n$=  2

Hence, by section formula

$x$ = $\frac{ mx_{2} +nx_{1}}{m+n}$

4=$\frac{(1*x)+(2*5)}{1+2}$

4=$\frac{x+10}{3}$

4*3=x+10

12=x+10

12-10=x

2=x

x=2

Hope it helps

Answer 2

Answer: x = 2.

Explanation:

The point which divides the line in ratio 1:2 internally made by co-ordinates (x, 3) and (5, - 4) is (4, 3). We need to find x.

We know,

Section formula = (mx1 + nx2/m + n, my1 + ny2/m + n)

where, m and n are 1:2.

Now,

x = mx1 + mx2/m + n

=> 4 = (x + 10)/(3)

=> x + 10 = 12

=> x coordinate = 2.

Therefore, the point is (2, 3).

More:

There are certain points which can divide a line externally.

For such cases, we use section formula as:

(mx1 - nx2/m - n, my1 - ny2/m - n).