Question

(a, b) is the mid-point of the line segment joining the point A (10, −6) and B (k, 4), and 3a − 2b = 26, then the value of k is ______.

Options

• 3

• 4

• 5

• 6

Answer 1

(a, b) is the mid-point of the line segment joining the point A (10, −6) and B (k, 4), and 3a − 2b = 26, then the value of k is 6.

Explanation:

Using the midpoint formula,

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

= `((10 + k) / 2, −1)`

Substitute b = −1 in 3a − 2b = 26:

3a + 2(−1) = 26,

3a + 2 = 26,

So, a = 8

Then,

`(10 + k) / 2` = 8

10 + k = 8 × 2

10 + k = 16

k = 16 − 10

∴ k = 6