Answer :
To find the midpoint of a line segment with endpoints \((-6, -3)\) and \((4, -7)\), follow these steps:
1. Identify the coordinates of the endpoints:
- Let the coordinates of the first endpoint be \((x_1, y_1) = (-6, -3)\).
- Let the coordinates of the second endpoint be \((x_2, y_2) = (4, -7)\).
2. Use the midpoint formula, which is given by:
[tex]\[ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
3. Substitute the coordinates into the midpoint formula:
[tex]\[ \text{Midpoint} = \left( \frac{-6 + 4}{2}, \frac{-3 + -7}{2} \right) \][/tex]
4. Perform the arithmetic inside the formula:
- Calculate the x-coordinate of the midpoint:
[tex]\[ \frac{-6 + 4}{2} = \frac{-2}{2} = -1 \][/tex]
- Calculate the y-coordinate of the midpoint:
[tex]\[ \frac{-3 + -7}{2} = \frac{-10}{2} = -5 \][/tex]
5. Combine these values to get the midpoint:
[tex]\[ \left( -1, -5 \right) \][/tex]
So, the midpoint of the line segment with endpoints \((-6, -3)\) and \((4, -7)\) is \((-1, -5)\).
Given the answer choices:
A. \((5, 1.5)\)
B. \((7, -5)\)
C. \((7.5, 5)\)
D. \((4.5, +)\)
The correct answer is not listed in the options, but according to our calculation, the midpoint should be [tex]\((-1, -5)\)[/tex].
1. Identify the coordinates of the endpoints:
- Let the coordinates of the first endpoint be \((x_1, y_1) = (-6, -3)\).
- Let the coordinates of the second endpoint be \((x_2, y_2) = (4, -7)\).
2. Use the midpoint formula, which is given by:
[tex]\[ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
3. Substitute the coordinates into the midpoint formula:
[tex]\[ \text{Midpoint} = \left( \frac{-6 + 4}{2}, \frac{-3 + -7}{2} \right) \][/tex]
4. Perform the arithmetic inside the formula:
- Calculate the x-coordinate of the midpoint:
[tex]\[ \frac{-6 + 4}{2} = \frac{-2}{2} = -1 \][/tex]
- Calculate the y-coordinate of the midpoint:
[tex]\[ \frac{-3 + -7}{2} = \frac{-10}{2} = -5 \][/tex]
5. Combine these values to get the midpoint:
[tex]\[ \left( -1, -5 \right) \][/tex]
So, the midpoint of the line segment with endpoints \((-6, -3)\) and \((4, -7)\) is \((-1, -5)\).
Given the answer choices:
A. \((5, 1.5)\)
B. \((7, -5)\)
C. \((7.5, 5)\)
D. \((4.5, +)\)
The correct answer is not listed in the options, but according to our calculation, the midpoint should be [tex]\((-1, -5)\)[/tex].
