Question

coordinate geometry the midpoint formula using this graph, how would adding 6+2 then dividing by 2 help you find the midpoint of line ( overline{ab} )? (1 point) it finds the average distance between the two y - values of points a and b. it finds the distance between points a and b it finds the sole midpoint of points a and b. it finds the average distance between the two x - values of points a and b.

Explanation:

1. First, identify the coordinates of points A and B. From the graph, point A has coordinates (2, -2) and point B has coordinates (6, 5).
2. The midpoint formula for the x - coordinate of two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(\frac{x_1 + x_2}{2}\), and for the y - coordinate is \(\frac{y_1 + y_2}{2}\).
3. Here, \(x_1 = 2\) (x - coordinate of A) and \(x_2=6\) (x - coordinate of B). The operation \(6 + 2\) then dividing by 2 is \(\frac{2 + 6}{2}\), which is the formula for finding the average of the x - values of points A and B. This average gives the x - coordinate of the midpoint of the line segment \(\overline{AB}\). The option "It finds the average distance between the two x - values of points A and B" is correct because adding the two x - values (2 and 6) and dividing by 2 is the way to find the average of the x - coordinates (which is related to the average distance in terms of the x - axis) to get the x - coordinate of the midpoint. The option "It finds the sole midpoint of points A and B" is incorrect because this operation only finds the x - coordinate of the midpoint, not the entire midpoint. The option about y - values is incorrect as 2 and 6 are x - values. The option about distance between A and B is incorrect as the distance formula is \(\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), not the average of x - values.

Answer:

It finds the average distance between the two x - values of points A and B.