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

Step-by-step 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}(-4+4)/(2),(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=(}(-4+0)/(2),(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=(}(0+4)/(2),(2-4)/(2)) \\ =(2,-1) \end{gathered}`

Therefore the coordinates of the