Question

Given A=(3,0) and B=(0,b-2). Find b if AB =5​

Answer 1

Answer:

b=6 or b= -2

Step-by-step explanation:

using distance formula

25=√(0-3)^2 +(b-2-0)^2

taking Square on both sides

equation becomes

b^2-4b-12=0

by factorisation

b^2-6b+2b-12=0

b(b-6)+2(b-6)=0

(b-6)(b+2)=0

b=6 or b=-2

Answer 2

Answer:

distance between any two points is given by Formula

distance²= (x1 -x2 )² +(y1 -y2 )²

A =(3,0) means

x1= 3 and y1 =0

B= (0, b-2) means

x2= 0 and y2= b-2

AB =5

5² = (3 -0)² +[ 0- (b-2)]²

25= 9 +b² -4b +4

b² -4b- 12=0

By solving this equation we get,

b = -2 , 6