Question

AB is a straight line of length 5 units. if A has co-ordinates (3,1) and B lies on y-axis. find co-ordinates of B.​

Answer 1

Answer:

As the point B lies on y-axis, x-co. of the point B must be 0.

So, let the co-ordinates of point B be ( 0, a ).

Distance between A and B is 5.

Using distance formula:

= > $\sqrt{(3-0)^2+(1-a)^2}=5$

= > 3^2 + (1-a)^2 = 5^2

= > (1-a)^2 = 5^2 - 3^2

= > ( 1 - a )^2 = 4^2

= > 1 - a = 4 or 1 - a = - 4

= > - 3 = a or a = 5

Hence the satisfying values of a are - 3 and 5.

Answer 2

Answer :

The length of AB = 5 units.

The co-ordinates of A are (3,1).

B lies on y axis, hence, x = 0.

Co-ordinates of B ?

Distance Formula : √{(x1 - x2)² + (y1 - y2)²}

⇒ √{(3 - 0)² + (1- y2)²} = 5

⇒ [(3)² + (1 - y2)²]² = 5²

⇒ 9 + (1 - y2)² = 25

⇒ (1 - y2)² = 25 - 9

⇒ (1 - y2) = √16

⇒ 1 - y2 = ±4

⇒ - y2 = ±4 - 1

⇒ - y2 = 3 or -5

⇒ y2 = - 3 or 5

Hence, co-ordinates of B is (0,-3) or (0,5).