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# Find the Coordinates of the Points Which Divide the Line Segment Joining the Points (-4, 0) and (0, 6) in Four Equal Parts. - CBSE Class 10 - Mathematics

ConceptConcepts of Coordinate Geometry

#### Question

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).

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Solution Find the Coordinates of the Points Which Divide the Line Segment Joining the Points (-4, 0) and (0, 6) in Four Equal Parts. Concept: Concepts of Coordinate Geometry.
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