Question

Find the ratio in which the point x,-1 divides the line segment joining the point -3 ,5 and 2,-5 also find the value of x

Answer 1

1. The ratio in which Point x,-1 divides the segment is m:n = 3:2 .
2. Also the value of x = 0

Answer 2

Answer:

The given point (x,-1) divides the line joining the points (-3,5) and (2,-5) in the ratio 3: 2, and the value of x is 0

Step-by-step explanation:

The section formula is

$P=(\frac{m(x2)+n(x1)}{m+n}, \frac{m(y2)+n(y2)}{m+n} )$

Let the point P(x,-1) divides the line joining the points A(-3,5) and B(2,-5) in the ratio

m: n, then using the section formula, we get

$(x,-1)=(\frac{2m-3n}{m+n}, \frac{-5m+5n}{m+n} )$

$-1 =\frac{-5m+5n}{m+n}$

- m - n = -5m + 5n

4m = 6n

m : n = 3 : 2

To find the value of x, consider

$x = \frac{2m-3n}{m+n}$

Put m = 3 and n = 2

$x = \frac{2(3)-3(2)}{3+2}$

x = 0

Therefore the point (x,-1) divides the line joining the points (-3,5) and (2,-5) in the ratio 3: 2, and the value of x is 0