316,176 views
33 votes
33 votes
The points A,B and C have coordinates (2,1), (b,3) and (5,5), where b>5 and angle ABC = 90 degrees. Find b.

User Samnau
by
2.5k points

1 Answer

20 votes
20 votes

Answer:

b=6

Explanation:

modul of the vector AB= sqrt((b-2)^2+(3-1)^2)= sqrt (b^2-4b+8). It is the length of the side AB

modul of the vector BC is equal to sqrt ((b-5)^2+(-2)^2)= sqrt (b^2-10b+29)

modul of the vector AC is sqrt ((5-2)^2+(5-1)^2)= 5

squared modul of AB + squared modul of BC = squared modul of the vector AC.

b^2-4b+8+b^2-10b+29=25

2b^2-14b+12=0

b^2-7b+6=0

b=1 b=6

b>5, s0 b=6

User Josh Sklare
by
2.6k points