Question

in what ratio does the poinr Y (-2 ,3 ) divided the line segment joining X (-4 , 1 ) and Z (3 ,13)​

Answer 1

Answer:

Step-by-step explanation:

Let the point Y (-2,3) divides the line segment joining X (-4,1) and Z (3,13) in the ratio m:n.

So, from section formula, coordinates of Y should be :

Y(a,b)  = {(mx2 + n x1)/ (m+n), (m y2 + ny1)/ (m+n)}

here, a = -2, b = 3, x1 = -4, y1  =1, x2 = 3, y2 = 13

Therefore,

-2 = {m*3+n*(-4) / (m+n)

On cross multiplication,

-2m - 2n = 3m - 4n

or, - 2m -3m = -4n +2n

or, -5m = -2n

or, 5m = 2n

or m/n = 2/5

or m:n = 2:5

Therefore, the point Y (-2,3) is dividing the line segment joining X (-4,1) and  (3,13) in the ratio 2:5.

Hope this will help you.

Thanks.