Locus of Points and Intersection of Loci

Givenpoints A(2, -3), B(2, 9), e(8, -3). and D(8, 9), fill in the blanks for questions 1-5 with adescription and coofjdinates or eouation . .1"••. sfa.c.e.1 fH;1, -~ c~ 8 ~ 't"0>; c4'--! 0)••• """ J I)G!;!; 0)

DescriptiQn In Q Plane In Space

4. (example) locus of points 5 c :r.c-Ie ~; tit. C~ ter (-S -.3) sflte..re \,J,'t" c..~~ runits from A I "- >'\ J ro.4; vS 5' L- J -3..•0) ~ n~ rA-d 'uS .s-II (~J-.3) :::ce note ) Y' =5 '

(X_~)ot + ()''''3Y~=;:"S' (X-.JY~+(y+3)~-t-a.;a::'~~5

5. locus of points :3 units fromD

t>C8jC;)

,-,WOe Ie, ..,..J \tt. ce ••1;~~(~.,) spl..-e.'I'c. w;·tJ. cen"tc.rGo. '" ct \1'" •• cl.'vs .3 (8; Cf 0) ••• cl l-Ad ;",s 3

~ 'J .:

(X-8').:l T (Y- ~).lz: 't " (x-s).1+( y -<1).1 + 7..l;:.'1.

6. XZ + yz\ =-16\. -

(sketch and describe the set ofpoints) . [. ).~

"" l..'''

c; r-c Ie w:'t J,. c..e.k-t e. yo

to) 0) _n d "r:::: I{-bLse less c.y I,' ~J e r ~ itlt_xis be-~....,~-~~IS

4." J.. r ",d : v.s 4

On 7-12 sketch, tcribe t~i>.locus of points and give an equation that describes the locus ofints

(6LSe-/~s.f c--l'.':l;der 1J VJ~"t:J.. e,..x," t "e,'h..) ~~ eo :. \l~-CJ-x:.s- a,,,,,cl ra.d,vs'J

6-".i tke.. 1! ca..)(; S

;'(;,[ OJ0) tA.. ttd c..; ,,:c,- e:~ ,0t'/.. c..e." ter (D., 0)

_hd r-...d,· «s ,(,J..

=- 3 (P.'.

7. 3 units from the set ofpoints described by. X2+ y,2= 9 _. t.-' •.c.-1e. "",;tAl ~e·~t-c.••..·~ A-..f..-,'--t:-'l~

l_)o) .,"J. r~ ~

8. 2 units from thr set ofpoints described b

jit

X2 + y2 = 16 • II 01-_ (,0. 0),. -tli c..e "'•..•.•r .Je-l ve- ~ \,oIIJ. I~cl yo;: 't

•;J bo.-s,c./es..s Co)' //hJ.er.s I

\,III j -t.1.. O-lC is a..S ~ - "'- ~. S

4. "CL r"'~: " ~ ..:.:'~c:l (,

9. equidistant fr01' the sets ofpoints described by c.errt~:(-.1)

(X_1)2 +(y+Z)Z =16, and ..J'I 1,. ,(x-l)Z +(y+zf = ~ -c« '141

c,~'r(..le. -w;tit. c..~t\i-er ,c>-~AVId ret.Jivs 3..f

Q< _() i. + Cy -t-~)ol:::(~:~)~

'.

y ::.X

},6-.fe-/ess c-i'l,·~.ter Lu i1:hOo-)f. j s .1. =r pi (1. r\ e. a....t(. -~ 0) ()..",d rc-J tos ~,~

) , ),

(X-I) ~.+-.(y+ ~):.l.~(:i.>~

y :: X+'I-

10. (exemple) equic!tistant fromthe sets of po.ints described byy=x+6andy= x+Z

11. ~id;stant .frolm the setsof points described by y = x + Zandy= x-Z I

I1Z. equidistant from the sets _ I , ~ e S

of points descri~ b~ x = .Z ../ 'Y + ~ ::. I (X.-;»' ). b "r-and y = -3. i,,,,,, ' 'I+3 -::.~' (X -.:::l)

"

.;a fl6.keS .'1+3-:' I (.x-.;l) Ory -to ~ -.:: - I C» -~)

y'?X-5" o:- •..•J y: -X,-I

Draw a diagram to find the locus of-points that satisfy the conditions. Then describe the locus14. all points in tHe coordinate plane 5 units 15. all points in the coordinate plane 6 units_-from the oriai"' an~ 3 units from the X""9_~. from tbg origin and -:g!lidi~lant fr~~2S:=-Qtld..f' D~~~_;> . ~ If>_l;-.TS Y..:m<:m "Ax 1I(3~~)

r ~ \ ••• ') L--d 8(3~-3.r.i)'"'.\. .~ Jc...:t. /1-("1.13) }t3 ('1.1-3',) I Co xn;:.... c.'-3h)-3.fi)

G ~,- 8 C (-+'j~) ~D (-<1-) -3) V' x::J,I:i. o C-,;-,n.,3r;J16. all the points in a plane equidistant from two 17. all points in a plane that ar@entimetersgiven points and ~uidistant_ from two parallel from a given line and 3 centimeters from a givenlines. _I I, J.' J spoint on the 'line. / . .'i't~,. rr" •.·',·tlc-~ - fU..F-f!." "r·" ~C> .,. Oc.us ' sf.lt: ....s t"l f -t:~e :>N4t.l-1 :'-se.c:. , '; ...• :.:; "-, ,;;~o:JD

&.odcl.;t~"I0\,,,, r--,e. . o ~ TTJ » J

18. all points in a plane that are 3 inches from a 19. ,all points in a plane that arwnches,from aqiven SeGment an ' equidistant from the two fl!ven line and 3 inches from a 9iv~int..an theendpoint' .1', d. ' . • -- 01- line A I" T.st 1'1 {D~V;::J ;r:O<5 :6~: DC; L~: .:

( . ,0, B I / -. ~~6'!"-_----i:.....-~

I,,[l