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
LGB 4042 G Scale Matra Yellow Construction Crane W OB
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LGB G SCALE McDonalds Ronald McDonald Box Car F P OB NEW 44910
LGB G SCALE McDonalds Ronald McDonald Box Car F P OB NEW 44910
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LGB G SCALE Campbells Soup Single Door Steel Box Car F P OB NEW 44911
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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
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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
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Lionel 8 87002 Large Scale G Gauge Santa Fe Grand Canyon Line OB MADE IN USA
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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
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Lionel 8 87809 Large Scale G Gauge Railbox Box Car OB Extra Couplers MADE IN USA
Lionel 8 87809 Large Scale G Gauge Railbox Box Car OB Extra Couplers MADE IN USA
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Lionel 8 87808 Large Scale G Gauge Union Pacific Searchlight Car OB MADE IN USA
Lionel 8 87808 Large Scale G Gauge Union Pacific Searchlight Car OB MADE IN USA
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LGB G Scale 4002 Kable Union Flatcar 2 Spools OB W Sleeve MADE IN GERMANY RARE
LGB G Scale 4002 Kable Union Flatcar 2 Spools OB W Sleeve MADE IN GERMANY RARE
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LGB G Scale 4067 D  R G Dark Brown Boxcar OB W Sleeve MADE IN GERMANY EX
LGB G Scale 4067 D R G Dark Brown Boxcar OB W Sleeve MADE IN GERMANY EX
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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
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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
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LGB G Scale  20680 Motorized Rail Truck Lettered LNE OB
LGB G Scale 20680 Motorized Rail Truck Lettered LNE OB
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LGB 4080 Y 01 G Scale Gauge Transcontinental Oil Company Tank Car w OB
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
LGB 4072 P01 G Scale Colorado Midland Refrigerator Line 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 G Scale Set 20530 Loco 2090Mercedes Truck  Work Trailer on Flat Cars OB
LGB G Scale Set 20530 Loco 2090Mercedes Truck Work Trailer on Flat Cars OB
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LGB G Scale  22010 Circus Handcar Excellent + Runs OB
LGB G Scale 22010 Circus Handcar Excellent + Runs 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
$55.00
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
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LGB 4073 C 03 G Scale DRGW Denver  Rio Grande High Side Gondola w OB
LGB 4073 C 03 G Scale DRGW Denver Rio Grande High Side Gondola w OB
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LGB 4061 G Scale DRGW Low Side Gondola w OB
LGB 4061 G Scale DRGW Low Side Gondola w OB
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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
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LGB G Scale 51120 Signalmans Hut Speed Controller LN OB
LGB G Scale 51120 Signalmans Hut Speed Controller LN OB
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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
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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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