Scale Ob

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 Steam Type Locomotive  Tender Both Units Powered  2017D OB Runs
LGB G Scale Steam Type Locomotive Tender Both Units Powered 2017D OB Runs
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LGB 3015 2ND CLASS PASSENGER CAR  G SCALE  OB
LGB 3015 2ND CLASS PASSENGER CAR G SCALE OB
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LGB 1982 JAHRESWAGEN 101ST ANNIVERSARY PASSENGER CAR  G SCALE  OB
LGB 1982 JAHRESWAGEN 101ST ANNIVERSARY PASSENGER CAR G SCALE OB
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LGB 4067 DG WILSON BROTHERS CIRCUS TENT  SUPPLY CAR G SCALE NEW OB
LGB 4067 DG WILSON BROTHERS CIRCUS TENT SUPPLY CAR G SCALE NEW OB
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USA Trains G Scale Northern Pacific OB Box Car 9105
USA Trains G Scale Northern Pacific OB Box Car 9105
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LGB 41090 G Scale RHB Axle Car Gondola w Wheel Load OB
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LGB 28003 RARE G Scale Rugen Shortline Steam Locomotive 994632 8 w OB
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LGB 2078 G Scale Corpet Lovet NO 51 Steam Locomotive 0 6 0 w OB
LGB 2078 G Scale Corpet Lovet NO 51 Steam Locomotive 0 6 0 w OB
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LGB 42124 G Scale Leuna DR Single Dome Tank Car w Brakemans Hut w OB
LGB 42124 G Scale Leuna DR Single Dome Tank Car w Brakemans Hut w OB
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LGB 42430 G Scale Field Railroad Tipple Car Red with Removable Coal w OB
LGB 42430 G Scale Field Railroad Tipple Car Red with Removable Coal w OB
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LGB 41430 G Scale Field Railroad Tipple Car Gray with Removable Coal w OB
LGB 41430 G Scale Field Railroad Tipple Car Gray with Removable Coal w OB
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LGB Lehmann 4046 G Scale Flat Car w Cable Drumm w OB
LGB Lehmann 4046 G Scale Flat Car w Cable Drumm w OB
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LGB 46405 G Scale Limited Edition ARAL Single Dome Tank Car w OB
LGB 46405 G Scale Limited Edition ARAL Single Dome Tank Car w OB
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LGB 4028 G Scale Kronenbourg Beer Box Car w OB
LGB 4028 G Scale Kronenbourg Beer Box Car w OB
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LGB 46400 G Scale BP British Petroleum Oil Single Dome Tank Car w OB
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LGB Marklin 94259 G Scale Stake Car w Unimog Vehicle Load w OB
LGB Marklin 94259 G Scale Stake Car w Unimog Vehicle Load w OB
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LGB 4040C G Scale Gauge BASF Single Dome Tank Car w OB
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LGB Lehmann 42125 G Scale DEA Single Dome Tank Car w OB
LGB Lehmann 42125 G Scale DEA Single Dome Tank Car w OB
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LGB Lehmann 4034 Cardinal Beer Box Car G Scale w OB
LGB Lehmann 4034 Cardinal Beer Box Car G Scale w OB
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LGB 23355 G Scale Sonderfahrt Motorized Trolley w OB
LGB 23355 G Scale Sonderfahrt Motorized Trolley w OB
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LGB 2150 G Scale Gauge Elis Tram 0 4 0 Steam Locomotive w OB
LGB 2150 G Scale Gauge Elis Tram 0 4 0 Steam Locomotive w OB
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LGB 21330 G Scale Gauge Track Maintenance Tractor Electric Engine w OB
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LGB 4032 G Scale Nestle Chocolate Platform Box Car w OB
LGB 4032 G Scale Nestle Chocolate Platform Box Car w OB
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LGB 2040 G Scale Brown Crocodile RhB 6 6 Electric Locomotive w OB
LGB 2040 G Scale Brown Crocodile RhB 6 6 Electric Locomotive w OB
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LGB 4042 G Scale Matra Yellow Construction Crane W OB
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BACHMANN BIG HAULERS G SCALE 95747 VICTOR GOLD MINING 20 GONDOLA CAR IN OB
BACHMANN BIG HAULERS G SCALE 95747 VICTOR GOLD MINING 20 GONDOLA CAR IN OB
$47.50
USA TRAINS G SCALE AMERICAN BAKING POWDER REFRIGERATOR REEFER R 16048 OB
USA TRAINS G SCALE AMERICAN BAKING POWDER REFRIGERATOR REEFER R 16048 OB
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LGB G SCALE 3080 DRGW DENVER  RIO GRANDE WESTERN PASSENGER CAR IN OB
LGB G SCALE 3080 DRGW DENVER RIO GRANDE WESTERN PASSENGER CAR IN OB
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G Scale LGB 47915 Union Pacific Box Car Nice Condition has OB TBJ157
G Scale LGB 47915 Union Pacific Box Car Nice Condition has OB TBJ157
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G Scale Aristo Craft ART 41306 Dupont Tank Car in OB TBJ158
G Scale Aristo Craft ART 41306 Dupont Tank Car in OB TBJ158
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LGB 4065 G Scale Gauge Rio Grande Caboose w OB
LGB 4065 G Scale Gauge Rio Grande Caboose w OB
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LGB 4036 G Scale Circus Animal Box Car w OB
LGB 4036 G Scale Circus Animal Box Car w OB
$45.00


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