Name___________________________________ Unit13ReviewSheet
Date__________________Per_______________ PerpendicularLines
1.
Mr.QuillhasprogrammedCharlietomovearoundtheclassroom,whichmeasures
feet.
feetby
a. Drawtheclassroomsetuponacoordinateplane
using
,
asthenortheastvertex.
b. Charliewasinitiallyplacedatposition ,
attime
t=1seconds,andhispositionattime
3seconds
is
,
.Representthisonthegraph.
c. HowfardidCharlietravelin seconds?
d. WhatisCharlie’sspeedtothenearesttenth?
e. AtwhattimedoesCharliestarthismovement?
f. AtwhatlocationdoesCharliestarthismovement?
g. WhatistheslopeofthelinecreatedbytheCharlie’spath?
h. WhatistheequationofthelinerepresentingCharlie’spath?
i. WhichwallwillCharliehitfirst?
j. DeterminethelocationwhereCharliewillhitthewall.
k. HowfarwillCharliehavetraveledoncehereachesthewall(tothenearesttenth)?
l. HowlongdidittakeCharlietoreachthewall(tothenearesttenthofasecond)?
2.
Arethepairsoflinesparallel,perpendicular,orneither?Explain.
a) 4x
5y
10and5x
4y
28
b) 3x
7y
42and 7x
3y
6
3.
Writetheequationofthelinepassingthrough 5, 2 andperpendicularto3
5
14.
4.
Writetheequationofthelinethrough
6, 8 and:
a) Parallelto
5
b)Perpendicular
c)Parallelto
3
d)Perpendicularto
LineAcontainspoints
3, 4 and
5
3
5.
6, 8 .LineBcontainsthepoints
, 6 and
2, 3 .
a) Findthevalueofkifthelinesareparallel.
b) Findthevalue(s)ofkifthelinesareperpendicular.
6.
Whatarethenewcoordinatesofthepoint 5, 2 ifitisrotatedabouttheorigin:
a) Counterclockwise90°?
b)Clockwise90°?
7.
UsingthegeneralformulaforperpendicularityofsegmentsthroughtheoriginO(0,0 ,determineif
segments and areperpendicular.
)
10, 2 ,
3,15 b)
3, 6 ,
4, 2 8.
Linesegment
connectspoints
4, 1 and
1, 2 .
a)WheredoespointMlandifthesegment
isrotated90°counterclockwiseabout ?
a) Wheredoespoint landifthesegmentis
rotated90°clockwiseabout ?
b) Whatistheslopeoftheoriginalsegment?
c)
Whatistheslopeoftherotatedsegments?
9. Given 6, 2 ,
a 9, 2 10, 1 ,and listedbelow,aresegments
and
b) 12, 10 perpendicular?
10. ShowthatthetrianglewiththeverticesD(–1,0),E(6,1)andF(2,4)isarighttriangle.
11. FindthecoordinatesofpointM,themidpointofthesegment
when
6, 5 and
3, 7 12. 2,
5 isthemidpointofsegment
.IfA’scoordinatesare(−5,3),whatarethecoordinatesofB?
13. Charlieisinaroomandchargingatposition 0, 3 .Oncecharged,hebeginsmovingonanortheast
pathataconstantspeedof2feetpersecondalongtheline6
90°andtravelsinthenewdirection.
8
18.After10seconds,itturnsleft
a) Drawasketchofthesituationbyplottingthegivenpoint.
b) Write6
8
18inslope‐interceptform.
c) Usetheequationfoundinpartbtodetermine4morepoints
x y
ontheline.Plotthesepoints.
3
6
9
12
d) Drawandlabelaslopeanddeterminethedistance
Charlietravelsbetweenpoints.
e) HowlongwillittakeCharlietotravelbetweeneachpairofpoints?
f) HowfardidCharlietravelin10seconds?
g) WhatarethecoordinatesofthepointatwhichCharliemadetheturn?
h) FindanequationforthesecondlinealongwhichCharlietraveled.
i) Ifafterturning,Charlietravelsfor7.5secondsalongthisline,howfarhasCharlietraveledsince
hisleftturn?
j) WhatisCharlie’slocation7.5secondsafterhisleftturn?
k) WhatistheequationofthelineCharlieneedstotravelalonginordertoreturnandrecharge?
l) HowfarisCharliefromthecharger?
m) HowlongwillittakeCharlietoreturntothecharger?
14. Given
4, 7 and
5, 3 :
a) Writeanequationforthenormallineto
,passingthroughS,instandardform
b) Writeanequationforthenormallineto
inslope‐interceptform
,passingthroughT,
15. Line istheperpendicularbisectorofsegmentBCwithB(−2,5)and (10,1).
a.Whatisthemidpointof
?
b.Whatistheslopeof
?
c.Whatistheslopeofline ?
d.Writetheequationofline ,theperpendicularbisectorof
.
16. Findthecoordinatesofthepoint,R,onthedirectedsegmentfrom
theratioof
a. 1:2
b. 2:3
4, 2 to
8, 5 thatdividesitin
17. GivenpointsA(‐5,23)andB(5,8),findthecoordinatesofpointCthatsits
1
ofthewayalong AB, 5
closertoAthantoB.
18. Findthedistancefromthelinetothepoint: 4 x  2 y  6  0;  3,8  19. Findthedistancefromthelinetothepoint: 3 y   x  7;  9, 4  20. FindthedistancefromP(‐1,5)toalinethatcontainspoints(4,‐3)and(‐6,3)
21. Findthedistancebetweenthepairofparallellineswiththegivenequations:
4 y  3 x  8  0 and 4 y  20  3 x 22. Showthatthequadrilateralwiththefollowingverticesisaparallelogram,butnotarectangle:
A  2,2  B  6,5 C  4, 0  D  4,  3 23. Showthatthequadrilateralwiththefollowingverticesisanisoscelestrapezoid:
A  a,0  B  a,0  C  b, c  D  b, c  24. ShowthatABCDisaparallelogramifA(–2,2),B(1,4)andC(2,8)andD(–1,6).
25. ShowthatDEFGisarhombusifD(2,2),E(5,–2)andF(9,1)andG(6,5).
26. FindthecircumcenterofatrianglewiththecoordinatesA(0,0),
B(6,0),C(6,4).
27. Findtheequationoftheperpendicularbisectorof AC ifthevertices
of ABC areA(‐3,2),B(5,2),andC(1,‐6). 28. Findthecoordinatesofthecentroidofatrianglewhoseverticesare
A(‐3,6),B(‐9,0),andC(9,0).
29. FindtheequationofthemedianfromvertexAintriangleABCwith
coordinatesA(‐3,0),B(1,0),andC(‐1,6).
30. Theverticesof PQR areP(0,0),Q(‐2,6),andR(4,0).Findthe
coordinatesoftheorthocenterof PQR .
31. FindtheequationofthealtitudefromvertexGin FGH with
coordinatesF(‐2,4),G(4,4)andH(1,‐2).