Question

find the co-ordinates of the points which divides the line segment joining the point(-4, 8) and (4, -4) into four equal parts

Answer 1

Answer:

Explanation:

Let's sketch the line segment as seen below;

From the above, we can see that points XYZ are the points that divide the line segment to four equal parts. Let's go ahead and determine their coordinates.

Since point Y is the midpoint of AB, we'll use the midpoint formula to determine its coordinate;

$\begin{gathered} \text{ Coordinates of Y = \lbrack}\frac{-4+4}{2},\frac{8+(-4)}{2}\rbrack \\ =(0,2) \end{gathered}$

We can see that point X is the midpoint of AY, let's use the midpoint formula too to determine its coordinates;

$\begin{gathered} \text{Coordinates of X=(}\frac{-4+0}{2},\frac{8+2}{2}) \\ =(-2,5) \end{gathered}$

We can see that point Z is the midpoint of YB, let's use the midpoint formula too to determine its coordinates;

$\begin{gathered} \text{Coordinates of Z=(}\frac{0+4}{2},\frac{2-4}{2}) \\ =(2,-1) \end{gathered}$

Therefore the coordinates of the