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]

Answer 1

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