To find the midpoint of a line segment AB with endpoints A(2, 7) and B(-3, -4), Fernando’s initial step of calculating 6.4 + (-2.5) appears to be incorrect since the points do not align with the coordinates provided for points A and B.
The correct steps to find the midpoint (M) are:
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Identify the coordinates of points A and B:
- A(2, 7) → x₁ = 2, y₁ = 7
- B(-3, -4) → x₂ = -3, y₂ = -4
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Use the midpoint formula: \[ M(x, y) = \left( \frac{x₁ + x₂}{2}, \frac{y₁ + y₂}{2} \right) \]
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Calculate the x-coordinate of the midpoint: \[ x = \frac{2 + (-3)}{2} = \frac{2 - 3}{2} = \frac{-1}{2} = -0.5 \]
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Calculate the y-coordinate of the midpoint: \[ y = \frac{7 + (-4)}{2} = \frac{7 - 4}{2} = \frac{3}{2} = 1.5 \]
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So the coordinates of the midpoint M are (-0.5, 1.5).
Given this context, since Fernando miscalculated based on the wrong approach, the correct next step should be:
Fernando should divide the sum of the correct x-values by 2, then repeat both steps using the y-values.
The appropriate choice based on the options you provided would likely align with this corrected next step, which ensures accurate calculations for both coordinates.