Question

Find the value of a if the distance between the point (a,2), (3,4) is 2 root 2

Answer 1

Answer is in the attachment.

Answer 2

Answer:

The value a comes out to be 1 and 5

Step-by-step explanation:

The formula of distance between two points is

A(x1, y1) and B(x2, y2)

is given by: d (A, B) = √ (x2 – x1)² + (y2 – y1)²

For finding distance between 2 points we get

AB² =( X2 -x1)² +(y2 -y1)²

AB² = (3-a)² +(4-2)²

= 9+a²-6a+16+4+16

= a²-6a +13

now AB² = (2√2)². - given

(2√2)² = a²-6a+13

4×2 = a²-6a+13

8= a²-6a+13

a²-6a+5=0

a²-5a-a+5=0

a(a-5) -1(a-5)=0

a-1(a-5) =0

a= 1 and a= 5.

(#SPJ2)