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Question
Draw a line segment AB of length 6 cm and mark a point X on it such that AX = `4/5` AB. [Use a scale and compass]
Solution
It is given that AX = `4/5` AB
i.e., `(AX)/(AB) = 4/5`
∴ `(AX)/(XB) = (AX)/(AB - AX) = 4/(5 - 4) = 1/4`
Thus, point X divides the line segment AB in the ratio 4:1
To draw a line segment AB of length 6 cm and mark a point X (using a scale and compass) such that `(AX)/(AB) = 4/5` i.e., `(AX)/(XB) = 4/1`, the following steps are to be followed:
Step 1: Draw a line segment AB of 6 cm and draw a ray AY making an acute angle with the segment AB.
Step 2: Locate 5(4 + 1) points i.e., A1, A2, A3, A4 and A5 on AY such that AA1 = A1A2 = ..... = A4A5·
Step 3: Join BA5.
Step 4: Through point A4, draw a line parallel to BA5 at A4 intersecting AB at point X.
Now, X is the required point on line segment AB of length 6 cm. This point satisfies the condition AX = `4/5` AB
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