Question 192942: I got this question on a test and i missed it
its about locus of points...
ther are 4 of them and i dont understand them at all!!
draw a sketch and write the equation for each locus
but i think i only really need the equation
the first says
locus of points equidistant from y= x+4 and passing through y=1 and y=7
2.
locus of points equidistant from (3,4) and (3,-2)
3.
locus points 5 units from origin
4.
locus of points 3 units from origin
and then there are 2 more from a different test.
83.
locus of points 4 units away from x= -2
84.
locus of point equidistant from y= -x+2 passing through y=4 and y=0.
if someone could help me i would be so thankful. homeschool and move alot so its hard for me to get help on my work. this site is a life saver!!
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! locus problems are great if you are good at visualization
loci around a point is a circle in a plane, and a sphere in space ok?
loci of 2 points is a line perpendicular to connecting line thru midpoint, in a plane.
In space this is harder to describe. visualize a sphere around one point, and then another sphere of same size around other point. If spheres just touch, it is a point. If they merge together more, it is circular plane.
loci around a line, is just two parallel lines equidistant from original line, in a plane.
in space, it is like a hollow tube,cylindrical surface, with the line as the center axis
1) Similar to # 84
remember loci in a plane of a line are parallel lines at equal distances from line.
Your problem did not specify how far apart, so we will just be convenient. you can modify to suit.
original line is y=x+4, draw a rough sketch. x-y coordinates. y intersect at 4, that is (0,4) point. slope is +1. IF we choose a line parallel to this but 3 units to right, we have y=x+1.
And the counterpart, 3 units to left is , y=x+7
at y=1, our loci coordinates are, (0,1) and (-6,1),,original (-3,1)
at y=7, loci,,(6,7) and (0,7),,original (3,7)
2) the midpoint between (3,4) and (3,-2) is (3,1) and line perpendicluar to connecting line is
y=(+1) Easier to just sketch roughly
3)loci is circle of radius 5 about origin. x^2+y^2=25 again sketch helps
4) same as (3) but radius =3, x^2 +y^2 =9
have you studied equation for circle is x^2+y^2=radius ^2
83) sketch helps, original line ,,x=(-2), is a vertical line thru (-2,0)
loci 4 units to right is x=(+2), and 4 units to left is, x=(-6)
Again both are vertical lines, parallel to original
84) Again, similar to (1)
sketching the original line, y intercept is (0,2),,slope(-1) y=-x+2
loci lines are parallel and equidistant, but again we do not know how far
lets use a transfer 3 right or left again
original eqn, y=-x+2, to left eqn y=-x-1, to right y=-x+5
generating coordinates we find original (2,0) right (5,0),, left (-1,0)
likewise (-2,4), (1,4), (-5,4)
Hopefully this is close to your needs
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