Short Answer 
The midpoint formula calculates the coordinates of a point dividing a line segment between two points based on a specified ratio. For points A(-1, 5) and B(6, 0) with a ratio of 2:1, the midpoint M is calculated as (11/3, 5/3).
Step 1: Understand the Midpoint Formula
The midpoint formula is used to find the coordinate of a point that divides a line segment between two points in a specific ratio. It can be written as:
- M(x,y) =(m*x1 + n*x2)/(m+n), (m*y1 + n*y2)/(m+n)
Here, x1 and x2 are the x-coordinates of the points A and B, and y1 and y2 are their respective y-coordinates. The m:n ratio indicates how the points are divided.
Step 2: Substitute the Given Values
In this case, you are given the coordinates of point A(-1, 5) and point B(6, 0) with a division ratio of 2:1. Substitute these values into the midpoint formula:
- M(x,y) = (1*(-1) + 2*(6))/(1 + 2)
- M(x,y) = (1*(5) + 2*(0))/(1 + 2)
This step involves plugging in the coordinates and the ratio into the formula to calculate the coordinates of point M.
Step 3: Calculate the Coordinates of Point M
Now, perform the operations to find the coordinates. For each part of M, calculate:
- M(x,y) = ( -1 + 12 ) / 3
- M(x,y) = ( 5 + 0 ) / 3
After solving these expressions, you will find that the coordinates of point M are (11/3, 5/3). This gives you the final point that divides the segment between A and B in the specified ratio.