To find the midpoint of line segment AB given points A(2, -2) and B(-5, 6), you use the midpoint formula, which calculates the average of the x-coordinates and the average of the y-coordinates of the points.
The formula for the midpoint (M) is: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
In this case:
- For the x-coordinates: \( x_1 = 2 \) and \( x_2 = -5 \)
- For the y-coordinates: \( y_1 = -2 \) and \( y_2 = 6 \)
Calculating the x-coordinate of the midpoint: \[ \frac{2 + (-5)}{2} = \frac{2 - 5}{2} = \frac{-3}{2} = -1.5 \]
Calculating the y-coordinate of the midpoint: \[ \frac{-2 + 6}{2} = \frac{4}{2} = 2 \]
So the midpoint M is (-1.5, 2).
Now, regarding the statement: "Using this graph, how would adding 6+2 then dividing by 2 help you find the midpoint of line AB?"
Adding 6 + 2 gives you 8, and dividing by 2 gives you 4. This operation doesn’t directly relate to the x-coordinates of points A and B, nor does it help in finding the y-coordinates. Therefore, the statement regarding finding the midpoint of points A and B doesn't hold logically in terms of the midpoint calculation.
The most accurate way to describe adding \( 6 + 2 \) then dividing by \( 2 \) in context of finding the midpoint of line AB is “It finds the average distance between the two y-values of points A and B,” since the numbers 6 and -2 are the y-values of point B and point A respectively, which aligns with the y-coordinate calculation in the midpoint formula.
So, the answer is: It finds the average distance between the two y-values of points A and B.
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