(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 ______.

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(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 $\times$ 2 10 + k = 16 k = 16 − 10 $\therefore$ k = 6

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