Question

the ratio in which x axis divides the line segment joining the points 5 4 and 2 - 3​

Answer 1

Answer:

4:3

hope this answer of mine helps you

Answer 2

Given: The x-axis divides the line segment joining the points (5,4) and (2,-3).

To find: The ratio in which the x-axis divides the line segment

Solution:The point of division lies on the x-axis. It should be in the form (x,0) because on the x-axis, the y-coordinate is always 0.

Therefore, the point of division=(x,0) where x can be any number.

Now, let point (5,4) be (x1, y1) and point (2,-3) be (x2, y2).

Let the ratio of division be k:1.

The coordinates of the point of division (x,y) is found using section formula which is:

$(x,y) = \frac{mx2 + nx1}{m + n} , \frac{my2 + ny1}{m + n}$

Here, m:n is the ratio of division. Therefore,

m = k and n = 1.

Putting the values in the section formula:

$(x,y) = \frac{k \times 2 + 1 \times 5}{k + 1} , \frac{k \times - 3 + 1 \times 4}{k + 1}$

$(x,y) = \frac{2k + 5}{k + 1} , \frac{ - 3k + 4}{k + 1}$

But the point of division is (x,0). Therefore, the y-coordinate should be 0.

Therefore,

$\frac{ - 3k + 4}{k + 1} = 0$

=> -3k+4=0

=> -3k = -4

=> k = 4/3

Therefore, the ratio of division

= k :1

= 4/3 : 1

= 4:3

Therefore, the x-axis divides the line segment in the ratio 4:3.