Question

find the ratio in which the line segment joining the point (1,-3) and (4,5) is divided by x axis. also find the point of division

Answer 1

Answer:

The point of intersection is $(\frac{17}{8},0)$.

Step-by-step explanation:

Let the line segment joining the point (1,-3) and (4,5) is divided by x axis is k:1 and the point of intersection be (x,0).

Section formula,

$P(x,y)=(\frac{mx_2+nx_1}{m+n}, \frac{my_2+ny_1}{m+n})$

Using section formula, we get

$\frac{my_2+ny_1}{m+n}=0$

$\frac{k(5)+1(-3)}{k+1}=0$

$5k-3=0$

$k=\frac{3}{5}$

The x-axis divides the line segment joining the point (1,-3) and (4,5) is 3:5.

Using section formula, we get

$\frac{mx_2+nx_1}{m+n}=\frac{3(4)+5(1)}{3+5}=\frac{17}{8}$

Therefore the point of intersection is $(\frac{17}{8},0)$.

Answer 2

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