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: Understanding the problem:
We are given two points: \( (-1, 3) \) and \( \left( 8, \frac{3}{2} \right) \), and we need to find the midpoint of the line segment joining these two points.

Step 2: Using the midpoint formula:
The formula for the midpoint \( M \) of a line segment joining two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:
\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] where: - \( (x_1, y_1) = (-1, 3) \), - \( (x_2, y_2) = \left( 8, \frac{3}{2} \right) \).

Step 3: Substituting the values into the midpoint formula:
Now, substitute \( x_1 = -1 \), \( y_1 = 3 \), \( x_2 = 8 \), and \( y_2 = \frac{3}{2} \) into the formula:
\[ M = \left( \frac{-1 + 8}{2}, \frac{3 + \frac{3}{2}}{2} \right) \] Simplify the expressions for the x and y coordinates:
For the x-coordinate:
\[ \frac{-1 + 8}{2} = \frac{7}{2} \] For the y-coordinate:
\[ \frac{3 + \frac{3}{2}}{2} = \frac{\frac{6}{2} + \frac{3}{2}}{2} = \frac{\frac{9}{2}}{2} = \frac{9}{4} \]

Step 4: Conclusion:
Therefore, the midpoint of the line segment joining the points \( (-1, 3) \) and \( \left( 8, \frac{3}{2} \right) \) is \( \left( \frac{7}{2}, \frac{9}{4} \right) \).