Question

The distance betwen points A = 1 + 1i and B = a + b is 5. Find the point B for each value provided below.

a. a = 4
b. b = 6

Answer 1

(a) 4+5i or, 4-3i

(b) 1+6i

Explanation:

The distance between the points A= 1+i, and B=a+bi is 5.

Therefore, we can write
`\sqrt{(a-1)^(2) +(b-1)^(2) } =5`

⇒
`(a-1)^(2) +(b-1)^(2) =25` ..... (1)

(a) If the value of a is 4, then from equation (1), we get

(4-1)²+(b-1)² = 25

⇒ (b-1)² =16

⇒ b-1 =±4

⇒ b= 5 or -3

Therefore, the point B will be represented by 4+5i or, 4-3i (Answer)

(b) If the value of b is 6, then from equation (1), we get

(a-1)²+(6-1)² = 25

⇒ (a-1)² =0

⇒ a = 1

Therefore, the point B will be represented by 1+6i. (Answer)