Question 28 of 40

What is the midpoint of a line segment with the endpoints [tex]\((-6, -3)\)[/tex] and [tex]\((9, -7)\)[/tex]?

A. [tex]\((-5, 1.5)\)[/tex]
B. [tex]\((-4.5, 1)\)[/tex]
C. [tex]\((1, -4.5)\)[/tex]
D. [tex]\((1.5, -5)\)[/tex]



Answer :

To find the midpoint of a line segment with given endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex], we use the midpoint formula. The midpoint [tex]\((M)\)[/tex] is given by:

[tex]\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]

Given the endpoints [tex]\((-6, -3)\)[/tex] and [tex]\(9, -7\)[/tex]:

Step-by-Step Solution:

1. Identify the coordinates of the endpoints:
- [tex]\((x_1, y_1) = (-6, -3)\)[/tex]
- [tex]\((x_2, y_2) = (9, -7)\)[/tex]

2. Plug these coordinates into the midpoint formula:
[tex]\[ M = \left( \frac{-6 + 9}{2}, \frac{-3 + (-7)}{2} \right) \][/tex]

3. Calculate each part separately:
- The [tex]\(x\)[/tex]-coordinate of the midpoint:
[tex]\[ \frac{-6 + 9}{2} = \frac{3}{2} = 1.5 \][/tex]
- The [tex]\(y\)[/tex]-coordinate of the midpoint:
[tex]\[ \frac{-3 + (-7)}{2} = \frac{-10}{2} = -5 \][/tex]

4. Combine these values to find the coordinates of the midpoint:
[tex]\[ M = (1.5, -5) \][/tex]

Therefore, the midpoint of the line segment with the given endpoints is [tex]\((1.5, -5)\)[/tex].

The correct answer is:
D. [tex]\((1.5, -5)\)[/tex]