Section Formula practice Questions (original) (raw)

Last Updated : 8 Jan, 2026

Section Formula is a mathematical tool used in coordinate geometry to determine the coordinates of a point that divides a line segment joining two given points in a given ratio. It is particularly useful in finding points that partition a segment either internally or externally in a specified ratio.

There are two cases for the section formula, i.e.,

Section Formula Practice Questions with Solution

These are some important Section Formula Practice Questions with Solution

**Question 1: The point P divides the line segment AB joining points A(2, 1) and B(-3, 6) in the ratio 2:3.

**Solution:

Given that A(2, 1)=(x1, y1), B(-3, 6) = (x2, y2)

Point P divides the segment AB in the ratio 2:3, hence m = 2, n = 3

Formula: **P(x, y) = {(mx 2 **+ nx 1 )/(m + n), (my 2 **+ ny 1 )/(m + n)}

Substituting all the known values,

P(x, y) ={[(2(-3)+3(2))/(2+3)],[(2(6)+3(1))/(2+3)]}

⇒ P(x, y) =[(-6+6/5), (12+3/5)]

⇒ P(x, y) = (0/5, 15/5)

⇒ P(x, y) = (0, 3)

**Question 2: A (4, 5) and B(7, – 1) are two given points and the point Y divides the line-segment AB externally in the ratio 4:3. Find the coordinates of Y.

**Solution:

Given that, A(4, 5) = (x1, y1), B(7, -1) = (x2, y2)

Point Y divides the segment AB in the ratio 4:3, hence m = 4, n = 3

Formula: **Y(x, y) = {(mx 2 - nx 1 )/(m - n), (my 2 - ny 1 )/(m - n)}

Substituting the known values,

Y(x, y) = {[(4(7)-3(4))/(4-3)],[(4(-1)-3(5)/(4-3)]}

⇒ Y(x, y) = {(28-12)/1,(-4-15)/1} ={16,-19}

The coordinates for the point Y are (16,-19).

**Question 3: Find the midpoint of AB where A(3, 4) and B(5, 7).

**Answer:

Given that, A(3, 5) = (x1, y1), B(4, 7) = (x2, y2)

Formula: M = {(x1 + x2)/2, (y1 + y2)/2}

Substituting the known values,

M = {(3 + 5)/2,(4 + 7)/2} ={8/2, 11/2} =( 4, 5.5)

The Midpoint of the AB is (4, 5.5).

**Question 4: Find the midpoint of AB where A(1, 4) and B(5, 8).

**Answer:

Given that, A(1, 4)=(x1, y1), B(5, 8) = (x2, y2)

Formula: P = {(x1 + x2)/2,(y1 + y2)/2}

Substituting the known values,

P={(1 + 5)/2,(4 + 8)/2} = {6/2, 12/2} = (3, 6)

The Midpoint of the AB is (3,6).

**Question 5: If a point P(k, 7) divides the line segment joining A(8, 9) and B(1, 2) in a ratio m : n then find values of m and n.

**Solution:

Given coordinates are A (8, 9) and B (1, 2)

Let the given point P (k, 7) divides the line segment in the ratio of m : 1

Using section formula for y coordinate.

⇒ 7 = (my2 + ny1)/(m + n )

⇒ 7 = (m × 2 + 1 × 9)/(m + 1)

⇒ 7 = (2m + 9)/(m +1)

⇒ 7m + 7 = 2m +9

⇒ 5m = 2

⇒ m = 5 / 2

So the required ratio is 5 : 2

Therefore, value of m is 5 and value of n is 2.

**Question 6: If a point P(k, 2) divides the line segment joining A(6, 8) and B(2, 3) in a ratio m : n then find values of m and n.

**Solution:

Given coordinates are A (6, 7) and B (2, 2)

Let the given point P (k, 2) divides the line segment in the ratio of m : 1

Using section formula for y coordinate.

⇒ 2 = (my2 + ny1)/(m + n )

⇒ 7 = (m × 2 + 1 × 8)/(m + 1)

⇒ 7 = (2m + 8)/(m +1)

⇒ 7m + 7 = 2m +8

⇒ 5m = 1

⇒ m = 1/5

So the required ratio is 1 : 5

Therefore, value of m is 1 and value of n is 5.

Section Formula practice Questions: Unsolved

**Question 1: The point P divides the line segment AB joining points A(-2, 1) and B(-3, 6) in the ratio 2:3.

**Question 2: A (5, 6) and B(2, – 1) are two given points and the point Y divides the line-segment AB externally in the ratio 5:3. Find the coordinates of Y.

**Question 3: The point P divides the line segment AB joining points A(5, 1) and B(-3, 6) in the ratio 1:1.

**Question 4: If a point P(2, p) divides the line segment joining A(8, 5) and B(2, 3) in a ratio m : n then find values of m and n.

**Question 5: The point P divides the line segment AB joining points A(-2, -1) and B(-3, -9) in the ratio 2:1.

**Question 6: If a point P(k, 3) divides the line segment joining A(4, 8) and B(5, 3) in a ratio m : n then find values of m and n.

**Question 7: A (-4, 5) and B(7, 1) are two given points and the point Y divides the line-segment AB externally in the ratio 2:3. Find the coordinates of Y.

**Question 8: If a point P(k, 4) divides the line segment joining A(2, 9) and B(1, 3) in a ratio m : n then find values of m and n.