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Coordinate geometry deals with the application of algebraic formulas to geometric concepts. It involves plotting points, lines, and shapes on a coordinate plane, which is a two-dimensional space defined by an x-axis and a y-axis. The coordinate plane allows us to describe the location of points using ordered pairs \((x, y)\). Each pair represents a point's distance from the origin (0,0), where the x-axis and y-axis intersect.
In coordinate geometry, we use various formulas to calculate distances, midpoints, and slopes of lines. Understanding these concepts helps us solve geometric problems using algebraic methods. Knowing how to work with coordinates is crucial for finding midpoints, among other things.

The midpoint formula is a key concept in coordinate geometry. It is used to find the point that is exactly halfway between two given points on a coordinate plane. The formula is: \[\text{Midpoint} = \bigg( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \bigg)\].
Let's break this down:

• \(x_1\) and \(x_2\) are the x-coordinates of the two endpoints.
• \(y_1\) and \(y_2\) are the y-coordinates of the two endpoints.

To find the midpoint, you add the x-coordinates of the endpoints and divide by 2. This gives you the x-coordinate of the midpoint. Likewise, add the y-coordinates and divide by 2 to get the y-coordinate of the midpoint.
Using the given endpoints (4, -3) and (-1, 3):

• Identify the coordinates: \(x_1 = 4, y_1 = -3 \)
• \(x_2 = -1, y_2 = 3\)
• Substitute into the formula:

\[\bigg( \frac{4 + (-1)}{2}, \frac{-3 + 3}{2} \bigg) = \bigg( \frac{3}{2}, \frac{0}{2} \bigg) = (1.5, 0)\]
So, the midpoint is (1.5, 0).

Arithmetic operations are basic mathematical processes: addition, subtraction, multiplication, and division. We often use these operations in coordinate geometry, especially when calculating midpoints.
In the midpoint formula, we add and divide:

• Add the x-coordinates of the endpoints: \(4 + (-1) = 3\)
• Add the y-coordinates of the endpoints: \(-3 + 3 = 0\)
• Divide the sum of the x-coordinates by 2: \(\frac{3}{2} = 1.5\)
• Divide the sum of the y-coordinates by 2: \(\frac{0}{2} = 0\)

These simple steps involve fundamental arithmetic operations that you likely already know. Correctly applying these allows us to accurately find the midpoint.
Remember, careful calculation ensures you correctly find the midpoint, leading to accurate solutions for more complex problems.
By understanding and practicing these arithmetic operations, you'll become more confident in solving geometry problems efficiently.