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

Answer: (D)

$\left(\frac{7}{2}, \frac{9}{4}\right)$

Answer 2

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:

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