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

The midpoint of a line segment joining two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:

\(\text{Mid-point} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)\)

Substitute the given points \((-1, 3)\) and \((8, 3)\):

\(\text{Mid-point} = \left( \frac{-1 + 8}{2}, \frac{3 + 3}{2} \right) = \left( \frac{7}{2}, \frac{6}{2} \right)\)

Simplify:
\(\text{Mid-point} = \left( \frac{7}{2}, 3 \right)\)

Thus, the correct answer is:

\(Option\space d)\ \left( \frac{7}{2}, \frac{9}{4} \right)\)