WORKSHEET ON SECTION FORMULA

1. Find the point which divides the line segment joining the points (3 , 5) and (8 , 10) internally in the ratio 2 : 3.

2. In what ratio does the point P(-2, 3) divide the line segment joining the points A(-3, 5) and B (4, -9) internally?

3. Find the points of trisection of the line segment joining the points (4, -1) and (-2, -3).

4. Find the coordinates of the point which divides the line segment joining (3, 4) and (–6, 2) in the ratio 3 : 2 externally.

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

1. Answer :

Let A(3, 5) and B(8, 10) be the given points.

Let the point P(x, y) divide the line AB internally in the ratio 2 : 3.

By section formula,

Here (x₁, y₁) = (3, 5), (x₂, y₂) = (8, 10), l = 2 and m = 3.

2. Answer :

Given points are A(-3, 5) and B(4, -9).

Let P (-2, 3) divide AB internally in the ratio l : m.

By the section formula,

Here (x₁, y₁) = (-3, 5) and (x₂, y₂) = (4, -9).

Equating the x-coordinates, we get

Hence P divides AB internally in the ratio 1 : 6.

3. Answer :

Let A(4, -1) and B(-2, -3) be the given points.

Let P(x, y) and Q(a, b) be the points of trisection of AB so that

AP = PQ = QB

Hence P divides AB internally in the ratio 1 : 2 and Q divides AB internally in the ratio 2 : 1.

By the section formula, the required points are

Note that Q is the midpoint of PB and P is the midpoint of AQ.

4. Answer :

Let A(3, 4) and B(-6, 2) be the given points.

Let the point P(x, y) divide the line AB externally in the ratio 3 : 2.

By section formula,

Here (x₁, y₁) = (3, 4), (x₂, y₂) = (-6, 2), l = 3 and m = 2.

5. Answer :

Let A(-4, 0) and B(0, 6) be the given points.

Let P, Q and R be the three points which divide the line AB into four equal parts.

P divides the line segment in the ratio 1 : 3.

By section formula, point P :

Q divides the line segment in the ratio 2 : 2.

By section formula, point Q :

R divides the line segment in the ratio 3 : 1.

By section formula, point R :

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