Short Answer 
The midpoint formula is used to find the dividing point of a line segment between two coordinates, A and B, in a specified ratio. Given the coordinates A(-1.5, 5) and B(6, 0) with a ratio of 2:1, the midpoint M is calculated to be (11/3, 5/3).
Step 1: Understand the Midpoint Formula
The midpoint formula is essential in coordinate geometry for finding the point that divides a line segment into a specific ratio. When dividing a segment between points A(x‚ÇÅ, y‚ÇÅ) and B(x‚ÇÇ, y‚ÇÇ) in the ratio of m:n, the midpoint M can be calculated using the formula:
- M(x, y) = (m/(m+n) * x‚ÇÅ + n/(m+n) * x‚ÇÇ, m/(m+n) * y‚ÇÅ + n/(m+n) * y‚ÇÇ)
Step 2: Identify Given Coordinates and Ratios
In this example, you have two coordinates: A(-1.5) and B(6) along with a division ratio of 2:1. It’s important to clearly define these elements before proceeding with calculations. Here:
- Coordinates: A(-1.5, 5) and B(6, 0)
- Ratio: 2 parts from A and 1 part from B
Step 3: Calculate the Midpoint Coordinates
Using the midpoint formula and the identified values, you can substitute into the equations to solve for M’s coordinates. Here’s how it is done:
- M(x, y) = (1(-1) + 2(6))/(1 + 2), (1(5) + 0)/(1 + 2)
- M(x, y) = (‚àí1 + 12)/3, (5 + 0)/3
- M(x, y) = (11/3, 5/3)
Thus, the possible coordinate of M is (11/3, 5/3).