Scale Ob

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Math question please help?

A triangle with vertices A (2, -4), B (1, 2), and C (4, -1) is dilated and the new triangle is located at A' (4, -8), B' (2, 4), and C' (8, -2). The dilation is ___________________ and the scale factor is _____________________.

A triangle with vertices A (2, -4), B (1, 2), and C (4, -1) is dilated and the new triangle is located at A' (4, -8), B' (2, 4), and C' (8, -2). The dilation is ___________________ and the scale factor is _____________________.
Question 5 answers
A.
a reduction 1/2
B.

a reduction; 2
C.

an enlargement; 2
D.
an enlargement 1/2

First draw a picture: http://www.flickr.com/photos/dwread/3732522936/

I've left out a few steps, because by now you know how to find the equation of a line from two points, and how to use the Pythagorean theorem to find the distance between two points.

Line joining B(1, 2) and B'(2, 4): y = 2x
Line joining A(2, -4) and A'(4, -8): y = -2x
Center of dilation, O, is the intersection of the lines: O(0, 0)

By the Pythagorean theorem,
OB = √(1²+2²) = √5
OB' = √(2²+4²) = √20 = 2√5

scale = OB'/OB = 2√5/√5 = 2
2 > 0 so the dilation is an enlargement and the scale factor is 2.

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LGB G Scale D  RG Box Car 4067 D 03 Made in Germany by Lehmann OB
LGB G Scale D RG Box Car 4067 D 03 Made in Germany by Lehmann OB
$44.95
LIONEL G SCALE POLAR EXPRESS SET 7 11022 OB PLUS CARTON
LIONEL G SCALE POLAR EXPRESS SET 7 11022 OB PLUS CARTON
$149.00
LGB G Scale Cardinal Beer Box Car Made in Germany by Lehmann Model  4034 OB
LGB G Scale Cardinal Beer Box Car Made in Germany by Lehmann Model 4034 OB
$29.99
Delton Locomotive Works Hoods Grade A Milk Reefer G Scale Car OB
Delton Locomotive Works Hoods Grade A Milk Reefer G Scale Car OB
$34.99
LGB 40810 G Scale Rhb Cargo Domizil Boxcar LN OB
LGB 40810 G Scale Rhb Cargo Domizil Boxcar LN OB
$49.99
LGB Lehmann 4034 Cardinal Beer Box Car G Scale w OB
LGB Lehmann 4034 Cardinal Beer Box Car G Scale w OB
$28.99
LGB G Scale 4472 Lake George  Boulder Brewing Co Reefer OB
LGB G Scale 4472 Lake George Boulder Brewing Co Reefer OB
$60.00
Lionel 8 87802 Large Scale G Gauge Conrail Box Car w ETD WOW OB MADE IN USA
Lionel 8 87802 Large Scale G Gauge Conrail Box Car w ETD WOW OB MADE IN USA
$58.99
Lionel 8 87104 Large Scale G Gauge Gerber Refer Refrigerator Car OB MADE IN USA
Lionel 8 87104 Large Scale G Gauge Gerber Refer Refrigerator Car OB MADE IN USA
$44.94
Lionel 8 87002 Large Scale G Gauge Santa Fe Grand Canyon Line OB MADE IN USA
Lionel 8 87002 Large Scale G Gauge Santa Fe Grand Canyon Line OB MADE IN USA
$42.49
Lionel 8 87100 Large Scale G Gauge Union Pacific Refer PFE OB MADE IN USA
Lionel 8 87100 Large Scale G Gauge Union Pacific Refer PFE OB MADE IN USA
$44.94
LGB G Scale 4068 D  R G Dark Green Stock Car OB W Sleeve MADE IN GERMANY EX
LGB G Scale 4068 D R G Dark Green Stock Car OB W Sleeve MADE IN GERMANY EX
$67.49
LGB Mrklin 24410 schienentraktor shunting Tractor TM 598 2 2 G Scale Mint OB
LGB Mrklin 24410 schienentraktor shunting Tractor TM 598 2 2 G Scale Mint OB
$536.47
LGB 3041 G Scale Gauge Sightseeing Car w OB MM
LGB 3041 G Scale Gauge Sightseeing Car w OB MM
$29.99
LGB Lehmann 4046 G Scale Flat Car w Cable Drumm w OB MM
LGB Lehmann 4046 G Scale Flat Car w Cable Drumm w OB MM
$29.99
LGB 4047 G Scale Flat Car With Keg Barrel Wine Vat Barrel w OB MM
LGB 4047 G Scale Flat Car With Keg Barrel Wine Vat Barrel w OB MM
$29.99
ARISTOCRAFT G SCALE SUMPTER VALLEY REFRIGERATOR CAR OB
ARISTOCRAFT G SCALE SUMPTER VALLEY REFRIGERATOR CAR OB
$29.95
LGB G Scale  22010 Circus Handcar Excellent + Runs OB
LGB G Scale 22010 Circus Handcar Excellent + Runs OB
$120.00
Aristo Craft G Scale ART 46114 Wawa Steel Stock Car C 7 w OB
Aristo Craft G Scale ART 46114 Wawa Steel Stock Car C 7 w OB
$50.00
Aristo Craft G Scale ART 46411 Bulkhead Flat Car C 7 w OB
Aristo Craft G Scale ART 46411 Bulkhead Flat Car C 7 w OB
$55.00
LGB G Scale  3000 2nd Class Passenger Coach Mint Probably never used OB
LGB G Scale 3000 2nd Class Passenger Coach Mint Probably never used OB
$55.00
Aristo Craft Trains 22110 Santa Fe Atsf P Diesel Locomotive G Scale Mint Ob
Aristo Craft Trains 22110 Santa Fe Atsf P Diesel Locomotive G Scale Mint Ob
$479.17
LGB 4061 G Scale DRGW Low Side Gondola w OB
LGB 4061 G Scale DRGW Low Side Gondola w OB
$49.99
Rare LGB 24420 G Scale RhB Ellock Ge 4 4 III Electric Locomotive w OB
Rare LGB 24420 G Scale RhB Ellock Ge 4 4 III Electric Locomotive w OB
$795.00
Bachmann 93433 Big Haulers G Scale Dads Rootbeer Single Dome Tank Car w OB
Bachmann 93433 Big Haulers G Scale Dads Rootbeer Single Dome Tank Car w OB
$29.99
LGB G Scale  4037 Circus Flat Casa Car OB
LGB G Scale 4037 Circus Flat Casa Car OB
$48.00
LGB G Scale  4165 Circus Caboose OB
LGB G Scale 4165 Circus Caboose OB
$60.00
Aristocraft G Scale Box Car 1999 East Coast Large Scale Show ART 46098OB
Aristocraft G Scale Box Car 1999 East Coast Large Scale Show ART 46098OB
$55.00
LGB G Scale  3125 Circus Open Air Observation Wagon OB
LGB G Scale 3125 Circus Open Air Observation Wagon OB
$85.00
LGB G Scale  4036 Circus Animal Cage Wagon OB
LGB G Scale 4036 Circus Animal Cage Wagon OB
$42.00
LGB G Scale  4038 Circus Flat Car with Big Cat Cage OB
LGB G Scale 4038 Circus Flat Car with Big Cat Cage OB
$45.00
RARE Early LGB 20401 G Scale Steam Freight Starter Set LN OB MM
RARE Early LGB 20401 G Scale Steam Freight Starter Set LN OB MM
$999.99


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