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What is the midpoint of a line segment with the endpoints [tex](-4, -3)[/tex] and [tex](7, -5)[/tex]?

A. [tex](1, -3.5)[/tex]
B. [tex](-4, 1.5)[/tex]
C. [tex](1.5, -4)[/tex]
D. [tex](-3.5, 1)[/tex]


Sagot :

To find the midpoint of a line segment given the endpoints [tex]\((-4, -3)\)[/tex] and [tex]\( (7, -5) \)[/tex], we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint [tex]\(M\)[/tex] of a line segment with endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] are given by:

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

Let's apply the formula step-by-step:

1. Identify the coordinates of the endpoints.
- The coordinates of the first endpoint [tex]\((x_1, y_1)\)[/tex] are [tex]\((-4, -3)\)[/tex].
- The coordinates of the second endpoint [tex]\((x_2, y_2)\)[/tex] are [tex]\((7, -5)\)[/tex].

2. Calculate the [tex]\(x\)[/tex]-coordinate of the midpoint:
[tex]\[ \text{x-coordinate} = \frac{x_1 + x_2}{2} = \frac{-4 + 7}{2} = \frac{3}{2} = 1.5 \][/tex]

3. Calculate the [tex]\(y\)[/tex]-coordinate of the midpoint:
[tex]\[ \text{y-coordinate} = \frac{y_1 + y_2}{2} = \frac{-3 + (-5)}{2} = \frac{-3 - 5}{2} = \frac{-8}{2} = -4 \][/tex]

Putting these two coordinates together, the coordinates of the midpoint are [tex]\( (1.5, -4) \)[/tex].

Therefore, the midpoint of the line segment with endpoints [tex]\((-4, -3)\)[/tex] and [tex]\((7, -5)\)[/tex] is [tex]\( \boxed{(1.5, -4)} \)[/tex]. Hence, the correct answer is:

C. [tex]\((1.5, -4)\)[/tex]