Question

find the co ordinates of points which divides the line segment joining a(-4,0) and b(0,6) into four equal parts

Answer 1

hope it helps you
please mark as brainlist

Answer 2

Answer:  The answer is (-3, 1.5), (-2, 3) and (-1, 4.5).

Step-by-step explanation:  As given in the question and shown in the attached figure, the line segment AB with end points A(-4,0) and B(0,6) are divided by the points C, D and E such that AC = CD = DE = EB.

The point C will divide AB in the ration 1 : 3, so its co-ordinates will be

$\textup{C}=\left(\dfrac{1\times 0+3\times (-4)}{1+3},\dfrac{1\times 6+3\times 0}{1+3}\right)=\left(-\dfrac{12}{4},\dfrac{6}{4}\right)=(-3,1.5).$

The point D will divide AB in the ration 1 : 1, so its co-ordinates will be

$\textup{D}=\left(\dfrac{0+(-4)}{2},\dfrac{6+0}{2}\right)=(-2,3).$

The point E will divide AB in the ration 3 : 1, so its co-ordinates will be

$\textup{E}=\left(\dfrac{3\times 0+1\times (-4)}{3+1},\dfrac{3\times 6+1\times 0}{3+1}\right)=\left(-\dfrac{4}{4},\dfrac{18}{4}\right)=(-1,4.5).$

Thus, the co-ordinates of the points are (-3, 1.5), (-2, 3) and (-1, 4.5).