how can i find a missing coordinate of one vertex of a triangle when given the other coordinates

Question

the points A,B and C have co-ordinates (2,1), (b,3) and (5,5) respectively, where b>3 and angle ABC = 90 degrees, find the value of the x co-ordinate labelled b

Answer 1

triangel...a=(2,1), B=(b,3), c=(5,5)

assume base is from a tu B

want 90 deg angel at B

Base slope...deltax=b-2, deltay=2, slope1=deltay/deltax=2/(b-2)

slope from B tu C...deltax=5-b, deltay=5-3=2, slope2=2/(5-b)

for 90 deg, slope2=-1/slope1=(2-b)/2....=2/(5-b)

(5-b)*(2-b)/2=2

(5-b)*(2-b)=4

b^2 -7b+10=4

b^2-7b-6=0

quadratik equashun giv b=7.7720019 or -0.7720019

me leev it tu yu tu chek if such make sens