Sliding Ladder
- Author:
- Sneha Titus
Questions that can guide you to visualize the locus:
i) If A(a,0) is a point on the x-axis and B (0,b) is a point on the y-axis and AB = 10, then what is the relationship between a and b?
Understanding the relationship between A and B
ii) When B is at the origin, what are the co-ordinates of A? And when A is at the origin, what are the co-ordinates of B?
Visualising the movement of the ladder
iii) If A moves along the positive direction of the x-axis, what is the direction of motion of B?
And where is the cat on the ladder?
iv) What are the co-ordinates of the mid-point M of AB in both the instances in question (ii)? What are the co-ordinates of the mid-point M of AB in terms of a and b?
v) What is the distance of M from the origin? Give your answer in terms of a and b. What is the numerical value of this distance? Hint: Use the answer to question (i).
vi) What can you say about the distance of M from the origin as A (and therefore B) move? Predict the locus of M as A moves along the x-axis.
vii) What changes if you consider the locus of any point on AB, instead of the mid-point? Right click on either of the other points shown on the ladder and choose Show Trace. Describe your observations.