anonymous
  • anonymous
i need to find coordinates of B. triangle ABC is right angle. A(-8,-3), C(0,3), AC=10 and CB=7.5
Mathematics
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schrodinger
  • schrodinger
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phi
  • phi
Is the right angle at B ? or do we have a choice of where to put the right angle ?
anonymous
  • anonymous
the right angle is at C
phi
  • phi
if you have a vector (a,b), the vector (-b,a) makes a counter-clockwise turn by 90º |dw:1378744459820:dw|

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phi
  • phi
If the right angle is at point C, we can do this: Find a vector that is perpendicular to the vector from A to C \( \vec{AC}\). Make this vector unit length, then scale it by 7.5. now add to the point C (0,3) to get to point B: B = (0,3) + 7.5 \( \vec{AC}\)
phi
  • phi
the vector from A to C is (0,3) - (-8,-3) = (8, 6) divide by the length 10 to get the unit vector (0.8, 0.6) turn c c w 90º to get (-0.6, 0.8) scale by 7.5: (7.5* -0.6, 7.5* 0.8) = (-4.5, 6) add to point (0,3): (0,3) + (-4.5,6) = (-4.5,9)
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