Question

find the ratio in which P(4,m) divides the line segment joining the points A(2,3) and B (6, - 3) . then find m

Answer 1

Answer:

The value of m is 0

Step-by-step explanation:

Point P(4,m) divides the line segment A(2,3) and B(6,-3)

Let point P divide AB into k:1

Using section formula,

$\text{Point A} (x_1,y_1) \text{ and Point B}(x_2,y_2) \text{ divide in ratio } m:n$

$x=\frac{mx_2+nx_1}{m+n}$

$y=\frac{my_2+yx_1}{m+n}$

Here, Ratio m:n = k:1 and point A(2,3) and B(6,-3) at P(4,m)

$4=\frac{6k+2}{k+1}$

$4k+4=6k+2$

$k=1$

Point P divide AB into 1:1 ratio.

$m=\frac{1(-3)+1(3)}{1+1}=0$

Thus, The value of m is 0

Answer 2

The value of m is 0

Step-by-step explanation:

AB is the line segment which id divided by the point P.

A(2, 3), B(6, -3) and P(4, m)

Let the ratio be k : 1

Using section formula,

$P(x, y)=\left(\frac{m x_{2}+n x_{1}}{m+n}, \frac{m y_{2}+m y_{1}}{m+n}\right)$

m : n = k : 1 and $x_1=2, y_1=3,x_2=6, y_2=-3$

$P(4, m)=\left(\frac{k\times6+1\times2}{k+1}, \frac{k\times(-3)+1\times3}{k+1}\right)$

$P(4, m)=\left(\frac{6k+2}{k+1}, \frac{-3k+3}{k+1}\right)$

Equate x-coordinates, we get

$4=\frac{6k+2}{k+1}$

4k + 4 = 6k + 2

4 - 2 = 6k - 4k

2 = 2k

1 = k

Equate y-coordinates, we get

$m=\frac{-3k+3}{k+1}$

$m=\frac{-3(1)+3}{1+1}$

m = 0

The value of m is 0.

To learn more...

1. Find the ratio in which P(4,m) divide the line segment joining the points A(2,3) and B(,6,-3) hence find m.

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2. Find the ratio in which p (4,m)divides the line segment joining the points A (2,3) and b (6, - 3) hence find m.

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