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Algebra
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Apr 27th, 2015

1.a) AB=sgrt((12-(-2))^2+(3-5)^2)=sgrt(200)

AC=sgrt((10+2)^2+(-11-5)^2)=20

BC=sgrt((10-12)^2+(-11-3)^2)=sgrt(200)

right triangle

(AB)^2+(BC)^2=(AC)^2

200+200=20^2

400=400

so the triangle is right

b) S=1/2 AB*BC

S=1/2*sgrt(200)*sgrt(200)=100

2. distanse = sgrt((2-(-4))^2+(2-(-3))^2)=sgrt(61) 

midpoint

x=(-4+2)/2=-1   y=(-3+2)/2=-1/2

midpoint (-1,-1/2)

Apr 27th, 2015

3. sgrt((x-4)^2+(y+3)^2)=6

(x-4)^2+(y+3)^2=6^2=36

the x-axis is y=0

(x-4)^2+3^2=36

x^2-8x+16+9=36

x^2-8x-11=0

D=sgrt(64+44)=sgrt(108)=6sgrt(3)

x1=(8+6sgrt(3))/2=4+3sgrt(3)

x2=(8-6sgrt(3))/2=4-3sgrt(3)

so (4+3sgrt(3),0) and (4-3sgrt(3),0)

Apr 27th, 2015

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