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BHHS0274

CSSA questions

unit Geometry nd Linear Functions

1) 2US-I-Si

w

OT

TO

SCALE

v

x

In the triangle

Wxv YZ =

9 cm, VX

=

12 cm,

WX =

8 cm and YZ

vx.

Prove that

.1

WZY is similar to

.1

UXVand find

the

length of WZ.t

2) ~ U S : ; 7 i i

D

OT

TO

SCALE

C

ABC and ABD are two triangles, X Yand Z are points such that XY IICB and YZ IIBD. Prove that

XY:

YZ

=

CB. BD.t

3)

2USfl-5i,

GL is a median in

.1

HFG and

HJ

FK.

a.

Draw a neat sketch

of

this diagram

on

your answer sheet.

b. Prove, giving reasons, that KL

LJ

OT TO

K

SCALE

H G

4) 2L90-2c

L

OT TO

SCALE

M

K

.1

KLM

is an isosceles triangle with KL

=

LM LLKM

=

80,

LNbisects L KLM

and

LKMN 20.

t.

On

your answer sheet, draw a neat sketch of the diagram above, showing all the given

information.

ii.

Find the size of

L LMN,

giving reasons for your answer.

111. Find the size

of L LNM,

giving reasons. t

5) 2U9()-5d

PQRS is a quadrilateral with

PR

QS, PQ..L

PS

and SR..L PS.

1.

On your answer sheet, draw a neat sketch and mark on it all the given information.

11. Prove that 8 QPS and 8 RSP are congruent.

iii. Hence prove that

PQRS

is a parallelogram.t

6) 2lJ4 lAc

EDUDATA

SOFTW RE PTY

l TD:1995 2010

tCSSA

NSW 1984 2003

7/25/2019 2U CSSA Geometry and Linear

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BHHS0274

n thediagramgivenbelow, ~ A B C isarightangletrianglewithL

BAC

90, CQ CR, PB

=

RB and

LACB =40.

A

B R

C

i.

Copythisdiagramontoyouranswerbooklet.

ii. Writedownthesizeof L PRQ. (Noreasonsarerequiredinyoursolution).t

7)

~ U 9 5 5 d

H = r L /

ThediagramshowsarhombusEFGH. AlineEL isdrawnthroughE sothatL HEL = 2xL FEL.

1.

Copythediagramontoyouranswerpage.

11

L

FGH

96 findthesize

of

L

ELF

givingreasons.

t

8) :::lJO]-3d

In thediagram,PQRS isaparallelogram. QR is producedtoU sothatQR = RU.

P

Q

S

- - - ~ \ - - - - - - - f

NOT TO

SC LE

1. Givingclearreasons,showthatthetriangles

PST

andURT arecongruent.

11.

Hence,

or

otherwise,showthat

T

isthemidpoint

ofSR.

t

9)

2UR4-2ii

Findtheequationof thelineperpendicularto2x - 3y - 6 0 andintersectingitonthex axis.t

lO)

2US4-3i\

Calculatetheperpendiculardistanceof thepoint(3, -1 fromtheline3x 4y 2 O.t

11) ~ U x 6 3 i i

Giventhepoints

-1,

2)and

B 3,

5)find:

a.

thelength

of

theintervaljoining

A

and

B.

b. thecoordinates

of

themidpoint

of

theinterval

AB.

c.

thegradient

of

thelineAB andhencetheangle

of

inclinationofAB tothepositivedirectionof

thex-axis.(Answertothenearestdegree.).

d. theequationofAB.t

12)

:::UR9-4

U

o

4

x

EDUDATA

SOFTWARE PTY

LTD:1995-2010 tCSSANSW 1984-2003

2

7/25/2019 2U CSSA Geometry and Linear

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BHHS0274

A

and

B

are the points

(0, 3)

and

4, -3)

respectively.

a. Find the distance between A and B.

b.

If C

is the point

-5, 0),

find the co-ordinates of

the

midpoint

of

the interval joining

Band C.

c. Show

that

the

equation

of

the line AB is 3x

+ 2y -

6 =

O

d. Hence find the equation of the line perpendicular to

AB

and passing through C.

e. Find the point

of

intersection

of

the line

AB with the

line

x - 4y + 5

O

f

Write

down

three inequalities to describe the shaded region given

above.t

l3)

2Ul)O4

A line, L, is inclined at an angle of

45

to the positive direction

of

the x-axis and passes through

the

point

X(O,

5).

1.

Show that

the

equation

of the

line

L

is

x - y + 5 = O

11. Line P is perpendicular to line

L. Show

that

the

gradient

of

line P is -1.

111. Show that the equation

of

the line

P,

through

Y(12, 5)

is x +Y =

17.

iv. Find the shortest distance between the line L and the point

Y(12, 5).

Leave your answer in surd

form with a rational denominator.

v.

The point Z

6, 11)

lies on the line L.

Show

that

6, 11)

is the point

of

intersection of the lines

LandP.

vi.

Show

that the distance between

Z

andXcan be expressed

in

the form a

J2

units.

vii. What type

of

triangle is XYZ?t

14)

2U94-2

The

line L has equation x + 2y =

5

and P is the point

(2, 4).

a. On

a

number

plane,

mark

the origin

0,

the point

P

and

draw the

line

L.

b. Find the midpoin t M, of

the

interval

OP.

c. Show

M lies on the line L.

d.

Find the gradients

of

the line

OP

and the line

L.

e. Show

the line L is

the

perpendicular bisector of the interval

OP.

f Line L meets the x-axis at Q. Find the co-ordinates of Q.

g.

A line is

drawn

through 0 parallel to

PQ

and it

meets

line

L in R.

Find the equation

ofOR.

h. Explain

why

PQOR is a rhombus.t

[pild

01

(l1l,]HAnswers)

1)

6 em

2) Proof

3) Proof

M

4)i)K

ii)

LLMN= 60

iii) LLNM 110

T>