Question

Given directed line segment AB determine point X on the graph such that X partions the segment A to B in a ratio of 1:4 and given its coordinates A(5,1) and b(-5,4)

(NEED THIS ASAP!!)

Answer 1

The coordinates of point X that divides the line in 1:4 are: (3,8/5)

Explanation:

When a point divides a line with coordinates (x1,y1) and (x2,y2) in ratio m:n,

the coordinates of point are given by:

`(x,y) = ((mx_2+nx_1)/(m+n) , (my_2+ny_1)/(m+n))`

Given points are:

(x1,y1) = (5,1)

(x2,y2) = (-5,4)

Putting the values in the formula

`X(x,y) = (((1)(-5)+(4)(5))/(1+4) , ((1)(4)+(4)(1))/(1+4))\\= ((-5+20)/(5), (4+4)/(5))\\=((15)/(5), (8)/(5))\\=(3,(8)/(5))`

Hence,

The coordinates of point X that divides the line in 1:4 are: (3,8/5)