Draw a diagram of the locus then write a description for it:
Point P lies on line l. What is the locus of points on l and 3cm from P?

Luke -
9th grade Geometry

Draw a diagram of the locus then write a description for it:
Point P lies on line l. What is the locus of points on l and 3cm from P?

You should have your line l in front of you.

Any point, 3 cm from P would be 3 cm from the line, since P could be on any point on the line.
The result will be two parallel lines to the line l, being on both of its side (the parallel lines 'sandwich' the line l) and semi circle at the edges of the line. The resulting shape is like a rectangle, but with circular width.

in the coordinate plane, how many points are both 5 units from the origin and 2 units from the x-axis?

Two points L and D are 8 units apart. How many points are equidistant from L and D and also 3 units from L

in the coordinate plane, how many points are both 5 units from the origin and 2 units from the x-axis?

Draw a sketch of the situation - it will help you see what's going on. All points that are 5 units from the origin lie on a circle with radius 5 centered on the origin. And all points that are 2 units from the x-axis lie along a line either at y = 2 or y=-2. Draw it out, see where the lines intersect, and post back with what you get for an answer.

two points L and D are 8 units apart. how many points are equidistant from L and D and also 3 units from L

Again - draw a sketch. Can you come up with any points that meet the criteria?