Thread: Locus of Points

(1) Point P is located on line AB.

(a) Describe the locus of points that are 3 units from line AB and (b) 5 points from point P.

(2) How many points satisfy both conditions in part (a) above?

Originally Posted by magentarita

(1) Point P is located on line AB.

(a) Describe the locus of points that are 3 units from line AB and (b) 5 points (maybe units?) from point P.

(2) How many points satisfy both conditions in part (a) above?

a) The locus of all points which are 3 units from a straight line are two parallels: One "above" and one "below"

b) The locus of all points with a constant distance to a fixed point is a circle.

Since and the radius of the circle is greater than the distance of the parallels to (AB) you'll get 4 points.

Originally Posted by earboth

a) The locus of all points which are 3 units from a straight line are two parallels: One "above" and one "below"

b) The locus of all points with a constant distance to a fixed point is a circle.

Since and the radius of the circle is greater than the distance of the parallels to (AB) you'll get 4 points.

Thanks for the great tips.