Find the coordinates of the points which divide the line segment joining the points (-4, 0) and (0, 6) in four equal parts.

#### Solution

The co-ordinates of the midpoint `(x_m, y_m)` between two points `(x_1, y_1)` and (x_2, y_2) is given by,

`(x_m,y_m) = (((x_1 + x_2)/2)"," ((y_1 + y_2)/2))`

Here we are supposed to find the points which divide the line joining *A*(-4*,*0) and *B*(0*,*6) into 4 equal parts.

We shall first find the midpoint *M*(*x, y*)* *of these two points since this point will divide the line into two equal parts

`(x_m, y_m) = (((-4+0)/2)","((0 + 6)/2))`

`(x_m, y_m) = (-2,3)`

So the point *M*(-2*,*3) splits this line into two equal parts.

Now, we need to find the midpoint of *A*(-4*,*0) and *M*(-2*,*3) separately and the midpoint of *B*(0*,*6) and *M*(-2*,*3). These two points along with *M*(-2*,*3) split the line joining the original two points into four equal parts.

Let M(e, d) be the midpoint of *A*(-4*,*0) and *M*(-2*,*3).

`(e,d) = (((-4-2)/2)","((0 + 3)/2))`

`(e,d) = (-3,3/2)`

Now let `M_2(g,h)` bet the midpoint of *B*(0*,*6) and *M*(-2*,*3).

`(g,h) = ((0 -2)/2)"," ((6 + 3)/2)`

`(g,h) = (-1, 9/2)`

Hence the co-ordinates of the points which divide the line joining the two given points are (-3,3/2), (-2, 3) and (-1, 9/2).