Question

(5,-1) and (6,9) midpoint and distance is: ____

Answer 1

The midpoint between the points (5,-1) and (6,9) is (5.5, 4), and the distance between them is approximately 10.05 units.

Step-by-step explanation:

Finding the Midpoint and Distance Between Two Points

To find the midpoint between two points, you take the average of the x-coordinates and the average of the y-coordinates of the given points. In the case of the points (5,-1) and (6,9), the midpoint M can be calculated as follows:

1. Mx = (x1 + x2) / 2 = (5 + 6) / 2 = 11 / 2 = 5.5
2. My = (y1 + y2) / 2 = (-1 + 9) / 2 = 8 / 2 = 4

So, the midpoint M is (5.5, 4).

To find the distance between two points, use the distance formula which derives from the Pythagorean theorem:

d = √((x2 - x1)^2 + (y2 - y1)^2)

For our points (5,-1) and (6,9), the distance d is calculated as:

d = √((6 - 5)^2 + (9 - (-1))^2)

d = √(1^2 + 10^2) = √(101) = 10.05 (approx)

The distance between the two points is approximately 10.05 units.