Question

The mid-point of the line segment joining (2k, 6) and (−4, −2) is (3, 2). The value of k is ______.

Options

• 2

• 3

• 4

• 5

Answer 1

The mid-point of the line segment joining (2k, 6) and (−4, −2) is (3, 2). The value of k is 5.

Explanation:

Using the midpoint formula:

midpoint = `((x_1 + x_2)/2, (y_1 + y_2)/2)`

For (2k, 6) and (−4, −2),

`(2k − 4)/2` = 3

2k − 4 = 6

2k = 10

∴ k = 5

The y-check `(6 + (−2))/2` = 2

So, k = 5