Question

If (a, b) is the mid-point of the line segment joining the points A(10, –6) and B(k, 4) and a – 2b = 18, then find the value of k.

Answer 1

Given: A(10, –6), B(k, 4), (a, b) is midpoint of AB and a – 2b = 18.

Step-wise calculation:

1. Midpoint formula:

`(a, b) = ((10 + k)/2, (-6 + 4)/2)`

= `((10 + k)/2, -1)`

Hence `a = (10 + k)/2` and b = –1.

2. Use a – 2b = 18:

`(10 + k)/2 - 2(-1) = 18` 

⇒ `(10 + k)/2 + 2 = 18` 

⇒ `(10 + k)/2 = 16`

3. Multiply both sides by 2:

10 + k = 32

⇒ k = 22