SOLUTION: Please help me solve this question. P(-3;10) and Q(3;4) are vertices of triangle PQR. If angle Q = 90 degrees determine the possible co-ordinates of R if QR = 4 sqrt( 2 ) Thanks

Algebra ->  Length-and-distance -> SOLUTION: Please help me solve this question. P(-3;10) and Q(3;4) are vertices of triangle PQR. If angle Q = 90 degrees determine the possible co-ordinates of R if QR = 4 sqrt( 2 ) Thanks       Log On


   

Question 418035: Please help me solve this question.
P(-3;10) and Q(3;4) are vertices of triangle PQR. If angle Q = 90 degrees determine the possible co-ordinates of R if QR = 4 sqrt( 2 )
Thanks :)
Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
The possible coordinates of R(x,y) are on the circle of radius +4%2Asqrt%282%29 and center point Q(3,4). The equation of the circle is: %28x-3%29%5E2%2B%28y-4%29%5E2=32+
The equation of line PQ is; y=-x+7 and the equation of line QR perpendicular to PQ
is: y=x+1. The possible coordinates of R(x,y) are on intersection of the line QR with circle. If we solve the system which contains these two equations: +y=x%2B1+and+%28x-3%29%5E2%2B%28y-4%29%5E2=32, we find coordinates of two points which are:
R[3+4*sqrt(2), 4+4*sqrt(2)] , R'[3-4*sqrt(2), 4-4*sqrt(2)]