Geometry, NAPX-I4-NC31 SA

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

711

Question

Shanti travels directly from from PP to RR as shown in the diagram below.



If she takes the route P→Q→RP → Q → R, how far extra does she travel?

Worked Solution

Using Pythagoras:
PR2PR^2 = QR2+QP2QR^2 + QP^2
= 502+120250^2 + 120^2
= 1302^2
PRPR = 130 m

∴\therefore Extra distance travelled

= 120 + 50 −- 130

= 40 m

Question Type

Answer Box

Variables

Variable nameVariable value
question
Shanti travels directly from from $P$ to $R$ as shown in the diagram below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2018/05/NAPX-I4-NC31.svg 290 indent vpad
If she takes the route $P → Q → R$, how far extra does she travel?
workedSolution
sm_nogap Using Pythagoras:
||| |-:|-| |$PR^2$|= $QR^2 + QP^2$| ||= $50^2 + 120^2$| ||= 130$^2$| |$PR$|= 130 m|

sm_nogap $\therefore$ Extra distance travelled >>= 120 + 50 $-$ 130 >>= {{{correctAnswer0}}} {{{suffix0}}}
correctAnswer0
40
prefix0
suffix0
m

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer040

m

Variant 1

DifficultyLevel

712

Question

Portia travels directly from from XX to ZZ as shown in the diagram below.



If she takes the route X→Y→ZX → Y → Z, how far extra does she travel?

Worked Solution

Using Pythagoras:
XZ2XZ^2 = XY2+YZ2XY^2 + YZ^2
= 72+2427^2 + 24^2
= 625
XZXZ = 25225^2
XZXZ = 25 km

∴\therefore Extra distance travelled

= 7 + 24 −- 25

= 6 km

Question Type

Answer Box

Variables

Variable nameVariable value
question
Portia travels directly from from $X$ to $Z$ as shown in the diagram below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/11/Geom_NAPX-I4-NC31-SA_v5b.svg 330 indent vpad
If she takes the route $X → Y → Z$, how far extra does she travel?
workedSolution
sm_nogap Using Pythagoras:
||| |-:|-| |$XZ^2$|= $XY^2 + YZ^2$| ||= $7^2 + 24^2$| ||= 625| |$XZ$|= $25^2$| |$XZ$|= 25 km|

sm_nogap $\therefore$ Extra distance travelled >>= 7 + 24 $-$ 25 >>= {{{correctAnswer0}}} {{{suffix0}}}
correctAnswer0
6
prefix0
suffix0
km

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer06

km

Variant 2

DifficultyLevel

714

Question

Chev travels directly from from MM to LL as shown in the diagram below.



If he takes the route M→N→LM → N → L, how far extra does he travel?

Worked Solution

Using Pythagoras:
ML2ML^2 = MN2+NL2MN^2 + NL^2
= 802+60280^2 + 60^2
= 1002^2
MLML = 100 m

∴\therefore Extra distance travelled

= 60 + 80 −- 100

= 40 m

Question Type

Answer Box

Variables

Variable nameVariable value
question
Chev travels directly from from $M$ to $L$ as shown in the diagram below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/11/Geom_NAPX-I4-NC31-SA_v3a.svg 230 indent vpad
If he takes the route $M → N → L$, how far extra does he travel?
workedSolution
sm_nogap Using Pythagoras:
||| |-:|-| |$ML^2$|= $MN^2 + NL^2$| ||= $80^2 + 60^2$ ||= 100$^2$| |$ML$|= 100 m

sm_nogap $\therefore$ Extra distance travelled >>= 60 + 80 $-$ 100 >>= {{{correctAnswer0}}} {{{suffix0}}}
correctAnswer0
40
prefix0
suffix0
m

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer040

m

Variant 3

DifficultyLevel

716

Question

Sean travels directly from from XX to YY as shown in the diagram below.



If he takes the route X→Z→YX → Z → Y, how far extra does he travel?

Worked Solution

Using Pythagoras:
XY2XY^2 = YZ2+ZX2YZ^2 + ZX^2
= 122+5212^2 + 5^2
= 132^2
XYXY = 13 km

∴\therefore Extra distance travelled

= 12 + 5 −- 13

= 4 km

Question Type

Answer Box

Variables

Variable nameVariable value
question
Sean travels directly from from $X$ to $Y$ as shown in the diagram below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/11/Geom_NAPX-I4-NC31-SA_v1b.svg 270 indent vpad
If he takes the route $X → Z → Y$, how far extra does he travel?
workedSolution
sm_nogap Using Pythagoras:
||| |-:|-| |$XY^2$|= $YZ^2 + ZX^2$| ||= $12^2 + 5^2$ ||= 13$^2$| |$XY$|= 13 km|

sm_nogap $\therefore$ Extra distance travelled >>= 12 + 5 $-$ 13 >>= {{{correctAnswer0}}} {{{suffix0}}}
correctAnswer0
4
prefix0
suffix0
km

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer04

km

Variant 4

DifficultyLevel

718

Question

Penny travels directly from from AA to CC as shown in the diagram below.



If she takes the route A→B→CA → B → C, how far extra does she travel?

Worked Solution

Using Pythagoras:
AC2AC^2 = AB2+BC2AB^2 + BC^2
= 62+826^2 + 8^2
= 102^2
ACAC = 10 km

∴\therefore Extra distance travelled

= 6 + 8 −- 10

= 4 km

Question Type

Answer Box

Variables

Variable nameVariable value
question
Penny travels directly from from $A$ to $C$ as shown in the diagram below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/11/Geom_NAPX-I4-NC31-SA_v4a.svg 240 indent vpad
If she takes the route $A → B → C$, how far extra does she travel?
workedSolution
sm_nogap Using Pythagoras:
||| |-:|-| |$AC^2$|= $AB^2 + BC^2$| ||= $6^2 + 8^2$| ||= 10$^2$| |$AC$|= 10 km|

sm_nogap $\therefore$ Extra distance travelled >>= 6 + 8 $-$ 10 >>= {{{correctAnswer0}}} {{{suffix0}}}
correctAnswer0
4
prefix0
suffix0
km

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer04

km

Variant 5

DifficultyLevel

720

Question

Bjorn travels directly from from BB to CC as shown in the diagram below.



If he takes the route C→A→BC → A → B, how far extra does he travel?

Worked Solution

Using Pythagoras:
BC2BC^2 = AC2+AB2AC^2 + AB^2
= 302+40230^2 + 40^2
= 502^2
BCBC = 50 m

∴\therefore Extra distance travelled

= 30 + 40 −- 50

= 20 m

Question Type

Answer Box

Variables

Variable nameVariable value
question
Bjorn travels directly from from $B$ to $C$ as shown in the diagram below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/11/Geom_NAPX-I4-NC31-SA_v2a.svg 290 indent vpad
If he takes the route $C → A → B$, how far extra does he travel?
workedSolution
sm_nogap Using Pythagoras:
||| |-:|-| |$BC^2$|= $AC^2 + AB^2$| ||= $30^2 + 40^2$| ||= 50$^2$| |$BC$|= 50 m|

sm_nogap $\therefore$ Extra distance travelled >>= 30 + 40 $-$ 50 >>= {{{correctAnswer0}}} {{{suffix0}}}
correctAnswer0
20
prefix0
suffix0
m

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer020

m

Tags

  • ms_ca