To divide a line segment AB in the ratio 5 : 6, draw a ray AX such that ∠BAX is an acute angle, then draw a ray BY parallel to AX and the points A_{1}, A_{2}, A_{3}, ....... and B_{1}, B_{2}, B_{3},....... are located at equal distances on ray AX and BY, respectively. Then the points joined are ______.

#### Options

A

_{5}and B_{6}A

_{6}and B_{5}A

_{4}and B_{5}A

_{5}and B_{4}

#### Solution

To divide a line segment AB in the ratio 5 : 6, draw a ray AX such that ∠BAX is an acute angle, then draw a ray BY parallel to AX and the points A_{1}, A_{2}, A_{3}, …….. and B_{1}, B_{2}, B_{3},………. are located at equal distances on ray AX and B_{4}, respectively. Then the points joined are **A _{5} and B_{6}**.

**Explanation:-**

To divide line segment AB in the ratio 5:6.

**Steps of construction:-**

**1.** Draw a ray AX making an acute ∠BAX.

**2.** Draw a ray BY parallel to AX by taking ∠ABY equal to ∠BAX.

**3. **Divide AX into five (m = 5) equal parts AA_{1}, A_{1}A_{2}, A_{2}A_{3}, A_{3}A_{4 }and A_{4}A_{5}

**4.** Divide BY into six (n = 6) equal parts and BB_{1}, B_{1}B_{2}, B_{2}B_{3}, B_{3}B_{4}, B_{4}B_{5} and B_{5}B_{6}.

**5.** Join B_{6 }A_{5}. Let it intersect AB at a point C. Then, AC : BC = 5 : 6