### Mathematics Class X

Real Numbers
Polynomials
Arithmetic Progressions
Triangles
Coordinate Geometry
Introduction to Trigonometry
Circles
Constructions
Areas Related to Circles
Surface Areas and Volumes
Statistics
Probability

# Division of a Line Segment

##### Method 1

AB is a line segment of 4 cm. Divide it in the ratio of 1:3 using a compass.

Steps of Construction

Step 1: Draw a line AC of any length by making an acute angle with the given line segment AB.

Step 2: Using any small length on the compass mark 4 points of equal size on AC, so that AX1 = AX2 = AX3 = AX4. We are marking 4 points as we have to divide the line in the ratio of 1:3, so 1 + 3 = 4.

Step 3: Now join BX4.

Step 4: Draw a line from point X1 to line AB parallel to BX4, which intersects AB at point P.

Now AP: PB = 1:3.

##### Method 2(Alternative Method)

A line can also be divided by another method.

Steps of Construction

Step 1: Draw a line AC with the acute angle with the line segment AB.

Step 2: Draw another line DB parallel to AC so that ∠BAX = ∠ADB

Step 3: Mark the points X1(m = 1) on AC and Y1, Y2, Yn = 3) on DB so that AX= BY= Y1Y= Y2Y3.

Step 4: Join X1Y3 so that it intersects line AB at P.

AP : PB = 1 : 3

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