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

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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 $\therefore$ k = 5 The y-check (6 + (−2))/2 = 2 So, k = 5

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