SOLUTION: one endpoint of a segment lies on the origin. if the second endpoints is known to lie on the line x=4, and the segment is a units long, explain how you could find the coordinates o

Algebra ->  Points-lines-and-rays -> SOLUTION: one endpoint of a segment lies on the origin. if the second endpoints is known to lie on the line x=4, and the segment is a units long, explain how you could find the coordinates o      Log On


   

Question 900532: one endpoint of a segment lies on the origin. if the second endpoints is known to lie on the line x=4, and the segment is a units long, explain how you could find the coordinates of the other endpoint
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
a is also a variable, but you would assume it has or could have a known value. a is a constant.

The distance from (0,0) to (4,y) must be a units.

Distance Formula for this, filled-in:
sqrt%28%284-0%29%5E2%2B%28y-0%29%5E2%29=a
sqrt%2816%2By%5E2%29=a
y%5E2%2B16=a%5E2
y%5E2=a%5E2-16
highlight%28y=-sqrt%28a%5E2-16%29%29 or highlight%28y=sqrt%28a%5E2-16%29%29

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The line +x=4+ is a vertical line through (4,0)
The line segment trough the origin is +a+
units long
--------------------
If I say that the intersection of the line segment
with +x=4+ is ( 4,y ), then the distance
between ( 0,0 ) and ( 4,y ) would be:
+a%5E2+=+%28+4+-+0+%29%5E2+%2B+%28+y+-+0+%29%5E2+
+a%5E2+=+4%5E2+%2B+y%5E2+
+y%5E2+=+a%5E2+-+16+
+y+=+sqrt%28+a%5E2+-+16+%29+
------------------------
So, the coordinates of the other endpoint are:
( 4 , sqrt( a^2 - 16 ) )