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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USA TRAINS G SCALE 1642 BUDWEISER BEER REFRIGERATOR CAR IN OB
USA TRAINS G SCALE 1642 BUDWEISER BEER REFRIGERATOR CAR IN OB
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USA TRAINS G SCALE 1643 BUSCH BEER REFRIGERATOR CAR IN OB
USA TRAINS G SCALE 1643 BUSCH BEER REFRIGERATOR CAR IN 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 G Scale D RG Box Car 4067 D 03 Made in Germany by Lehmann 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 4055 Beton ConstructionCement Concrete Mixer Flat Car w OB NIB G Scale
LGB 4055 Beton ConstructionCement Concrete Mixer Flat Car w OB NIB G Scale
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LGB 5033 50330 TRANSIT TRAIN STOP SIGN SET G SCALE IN OB
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LGB Lehmann 4076 X01 G Scale Peabody Short Line Hopper w Load w OB
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LGB 4073 C 03 G Scale DRGW High Side Gondola w OB
LGB 4073 C 03 G Scale DRGW High Side Gondola w OB
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LGB 41720 G Scale Annie Oakley Refrigerator Reefer Car w OB
LGB 41720 G Scale Annie Oakley Refrigerator Reefer Car w OB
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LGB 40022 G Scale Ernst Heinrichsen Museum Car w OB
LGB 40022 G Scale Ernst Heinrichsen Museum Car w OB
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G Scale USA TRAINS R17412 Conrail Center Beam Flat Car with OB TBJ132
G Scale USA TRAINS R17412 Conrail Center Beam Flat Car with OB TBJ132
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G Scale Aristo Craft ART 41306 Dupont Tank Car in OB TBJ137
G Scale Aristo Craft ART 41306 Dupont Tank Car in OB TBJ137
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Railway Express Agency Diesel Locomotive FA 1 G Scale PRR 9621 IN OB
Railway Express Agency Diesel Locomotive FA 1 G Scale PRR 9621 IN OB
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LGB G Scale Set 20530 Loco 2090Mercedes Truck Work Trailer on Flat Cars OB
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G Scale LGB 4267S LGB LAKE GEORGE  BOULDER BOX CAR WITH DIESEL SOUND IN OB
G Scale LGB 4267S LGB LAKE GEORGE BOULDER BOX CAR WITH DIESEL SOUND IN OB
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LGB G Scale 44673 Sitting Bull Native American Legend Box Car OB
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LGB G Scale 4328 der Gute Appenzeller Kase Box Car 4 Wheels OB
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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
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LGB G SCALE 30570 DELUXE SANTA FE PASSENGER CAR 30 LONG IN OB HARD TO FIND
LGB G SCALE 30570 DELUXE SANTA FE PASSENGER CAR 30 LONG IN OB HARD TO FIND
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LGB 41090 G Scale RHB Axle Car Gondola w Wheel Load OB
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
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 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
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 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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