Question

The midpoint of line segment joining (x, y) and (-7, 5) is (4, 6). Then x=,y=

• A. \(\left(-\frac{3}{2}, \frac{11}{2}\right)\)
• B. (15,-7)
• C. (11, 1)
• D. (15,7)

Answer 1

The Correct Option is B

We are given the midpoint of the segment joining \((x, -y)\) and \((-7, 5)\) is \((4, 6)\).\\ Midpoint formula: \[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Here, \[ (x_1, y_1) = (x, -y),\quad (x_2, y_2) = (-7, 5),\quad \text{Midpoint} = (4, 6) \] Apply the formula: \[ \frac{x + (-7)}{2} = 4 \Rightarrow \frac{x - 7}{2} = 4 \Rightarrow x - 7 = 8 \Rightarrow x = 15 \] \[ \frac{-y + 5}{2} = 6 \Rightarrow -y + 5 = 12 \Rightarrow -y = 7 \Rightarrow y = -7 \]

The correct option is (B): \((15,-7)\)