Question

i need to find coordinates of B. triangle ABC is right angle. A(-8,-3), C(0,3), AC=10 and CB=7.5

Answer 1

Is the right angle at B ? or do we have a choice of where to put the right angle ?

Answer 2

the right angle is at C

Answer 3

if you have a vector (a,b), the vector (-b,a) makes a counter-clockwise turn by 90º

Answer 4

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 \( \vec{AC}\)

Answer 5

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)