Question

The mid-point of the line segment joining the points \((-1, 3)\) and \(\left(8, \frac{3}{2}\right)\) is:

• A. \(\left(\frac{7}{2}, -\frac{3}{4}\right)\)
• B. \(\left(\frac{7}{2}, \frac{9}{2}\right)\)
• C. \(\left(\frac{9}{2}, -\frac{3}{4}\right)\)
• D. \(\left(\frac{7}{2}, \frac{9}{4}\right)\)

Answer 1

The Correct Option is D

Step 1: Use the midpoint formula
The midpoint \( M \) of a line segment joining two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:
\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]

Step 2: Substitute the given points
Let \( (x_1, y_1) = (-1, 3) \) and \( (x_2, y_2) = \left(8, \frac{3}{2} \right) \)

Step 3: Calculate the x-coordinate of the midpoint
\[ \frac{-1 + 8}{2} = \frac{7}{2} \]

Step 4: Calculate the y-coordinate of the midpoint
\[ \frac{3 + \frac{3}{2}}{2} = \frac{\frac{6}{2} + \frac{3}{2}}{2} = \frac{\frac{9}{2}}{2} = \frac{9}{4} \]

Final Answer:
\[ \left( \frac{7}{2}, \frac{9}{4} \right) \]