To find the midpoint of a line segment defined by two points \(A(2,-2)\) and \(B(6,5)\), you use the midpoint formula, which calculates the average of the x-coordinates and the average of the y-coordinates.
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Finding the x-coordinate of the midpoint:
- The x-coordinate of the midpoint is calculated as: \[ \text{Midpoint}_x = \frac{x_A + x_B}{2} = \frac{2 + 6}{2} = \frac{8}{2} = 4 \]
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Finding the y-coordinate of the midpoint:
- The y-coordinate is calculated similarly: \[ \text{Midpoint}_y = \frac{y_A + y_B}{2} = \frac{-2 + 5}{2} = \frac{3}{2} = 1.5 \]
So, the midpoint \(M\) of the line segment \(AB\) is \(M(4, 1.5)\).
Answer Selection
Now, looking at your options regarding what the calculation of adding 5 and -2, then dividing by 2, helps achieve:
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It finds the y value that is average between the two y values of points.
- This is correct when it refers to calculating the y-coordinate of the midpoint.
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It finds the sole midpoint of points A and B.
- This statement is a bit vague—it suggests finding the entire midpoint rather than distinguishing between x and y.
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It finds the x value that is the average between the two x values of points.
- This is correct when it refers to calculating the x-coordinate of the midpoint.
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It finds the distance between points A and B.
- This is incorrect; the average does not directly give distance.
Based on the specific question regarding \(5\) and \(-2\), that refers directly to the y-coordinates of points A and B, making the best answer "It finds the y value that is average between the two y values of points."
1 answer