Locus New Senior Mathematics Fitzpatrick 2 Unit for 11&12 page 229. (1 Viewer)

[revoniscence]

This is a question from New Senior Mathematics Fitzpatrick 2 Unit for 11&12 page 229.
The question states a ladder that is 6m long rests with one end on the horizontal ground, and the other end against a vertical wall. Considering the ground and the wall as the X- and Y -Axes repsectively, find the locus of the midpoint of the ladder.
Can anybody please help me. Thanks.

 

[watatank]

I'm not entirely sure if this is correct, seeing as I worked this out through drawing a diagram and logic rather than algebra....I *think* the answer is

x^2 + y^2 = 9 (x, y > 0)


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Well its an arc from (0,3) to (3,0)... or the crosses as shown on that vague diagram... why those points? those points are the midpoints when the ladder is lay down on the ground and pushed up against the wall.

I think that answer is correct, its a circle but it counts only the points in the first quadrant.

 

[webby234]

Yeah sounds right - the midpoint of the ladder must always be 3m from the origin (as the length of the ladder is 6m) so it's a circle with centre at the origin and a radius of 3 (ie X² + Y² = 3² = 9). X and Y must be positive so only include the first quadrant.