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 A₁, A₂, A₃, ... and B₁, B₂, B₃, ... are located at equal distances on rays AX and BY, respectively. Then the points joined are
A5 and B6
A6 and B5
A4 and B5
A5 and B4
Step 1: We want to divide the line segment AB in the ratio 5:6. This means that if we cut AB at some point P, then AP : PB = 5 : 6.
Step 2: To do this, we draw a ray AX from point A making an acute angle with AB. On this ray, we mark equal distances and label them as A₁, A₂, A₃, …
Step 3: Similarly, we draw another ray BY from point B parallel to AX. On this ray also, we mark equal distances and label them as B₁, B₂, B₃, …
Step 4: Now, to divide in the ratio 5:6, we need to take the 5th point on AX (that is A₅) and the 6th point on BY (that is B₆).
Step 5: Join A₅ to B₆. The line A₅B₆ will intersect AB at a point P. This point P divides AB in the required ratio 5:6.
Final Answer: The correct points to join are A₅ and B₆.