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 4042 G Scale Matra Yellow Construction Crane W OB
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LGB G SCALE 30570 DELUXE SANTA FE PASSENGER CAR 30 LONG IN OB
LGB G SCALE 30570 DELUXE SANTA FE PASSENGER CAR 30 LONG IN OB
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RAILKING 1 32 G SCALE AMTRAK SMOOTH SIDED DOVE TAIL OBSERVATION CAR OB
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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
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LGB 2078 G Scale Corpet Lovet NO 51 Steam Locomotive 0 6 0 w OB
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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
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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 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 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
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LGB 23355 G Scale Sonderfahrt Motorized Trolley w OB
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LGB G Scale Set 20530 Loco 2090Mercedes Truck Work Trailer on Flat Cars OB
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LGB G Scale 20680 Motorized Rail Truck Lettered LNE OB
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LGB Mrklin 24410 schienentraktor shunting Tractor TM 598 2 2 G Scale Mint OB
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LGB 4080 Y 01 G Scale Gauge Transcontinental Oil Company Tank Car w OB
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LGB Lehmann Gross Bahn 42125 DEA Single Dome Tank Car w OB G Scale
LGB Lehmann Gross Bahn 42125 DEA Single Dome Tank Car w OB G Scale
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LGB 44408 G Scale Substral Single Dome Tank Car w OB
LGB 44408 G Scale Substral Single Dome Tank Car w OB
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LGB 3072 G Scale Florida Boy Orange Passenger Car w OB
LGB 3072 G Scale Florida Boy Orange Passenger Car w OB
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LGB G Scale 43880 RhB High Side Wooden Gondola w OB
LGB G Scale 43880 RhB High Side Wooden Gondola w OB
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LGB 4072 P01 G Scale Colorado Midland Refrigerator Line Car w OB
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LGB 4040 G Scale ARAL Blue Single Dome Petroleum Tank Car w OB
LGB 4040 G Scale ARAL Blue Single Dome Petroleum Tank Car w OB
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LGB 3015 G Scale Second Class 2 Blue  Cream Coach Passenger Car w OB
LGB 3015 G Scale Second Class 2 Blue Cream Coach Passenger Car w OB
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LGB 36815 G Scale WPY Royal Mail Passenger Car 202 w OB
LGB 36815 G Scale WPY Royal Mail Passenger Car 202 w OB
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LGB TRAINS G SCALE 4036 CIRCUS STOCK CAR IN OB
LGB TRAINS G SCALE 4036 CIRCUS STOCK CAR IN OB
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LGB 4165 Circus Caboose G Scale w OB  Sleeve NOS New Old Stock
LGB 4165 Circus Caboose G Scale w OB Sleeve NOS New Old Stock
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LGB 4036 Circus Animal Wagon Car G Scale Lighted w OB  Sleeve NOS
LGB 4036 Circus Animal Wagon Car G Scale Lighted w OB Sleeve NOS
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LGB Lehmann 43880 G Scale RhB High Side Wooden Gondola w OB
LGB Lehmann 43880 G Scale RhB High Side Wooden Gondola w OB
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LGB 40140 G Scale RhB Refuse Manual Dump Car w 2 Containers 9040 w OB
LGB 40140 G Scale RhB Refuse Manual Dump Car w 2 Containers 9040 w OB
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LGB 4127 G Scale Cargo Domizil RHB Box Car w OB
LGB 4127 G Scale Cargo Domizil RHB Box Car w OB
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LGB 36076 G Scale 1996 Christmas Train Passenger Coach Car w OB
LGB 36076 G Scale 1996 Christmas Train Passenger Coach Car w OB
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