Page 2 - Lesson Note 1- ch 11 Division of line segment (Contruction)

Division of a line segment

Q. 1 Divide a line segment 6 cm long in the ratio 4 : 3.

Sol.

Steps of Construction:
(a) Draw a line segment AB = 6 cm.
(b) Draw a ray AX, making an acute angle BAX.
(c) Along AX, mark (4 + 3) = 7 points A1, A2, A3, A4, A5, A6 and A7 such that AA1 =
A1A2 = A2A3 = A3A4 = A4A5 = A5A6 = A6A7
(d) Join A7B.
(e) From A4 draw A4C||A7B, meeting AB at C.
Then, C is the point on AB, which divides it in the ratio 4 : 3.
Thus, AC : CB = 4 : 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, Y3 n = 3) on DB so that AX1 = BY1 = Y1Y2 =
Y2Y3.
Step 4: Join X1Y3 so that it intersects line AB at P.

AP:PB = 1:3

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