Rectangular Coordinates

Rectangular coordinates, also known as Cartesian coordinates, are used to locate points in a two-dimensional plane using a pair of numbers (x, y). The x-coordinate represents the horizontal position of a point, and the y-coordinate represents the vertical position of the point.

Graphing Points

To graph a point using rectangular coordinates, locate the point on the plane by moving horizontally (x) and then vertically (y) to the specified coordinates. For example, the point (3, 4) would be located 3 units to the right and 4 units up from the origin (0, 0).

Distance Formula

The distance between two points (x1, y1) and (x2, y2) can be found using the distance formula:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Midpoint Formula

The midpoint between two points (x1, y1) and (x2, y2) can be found using the midpoint formula:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Practice Problems:

1. Graph the points (2, 5) and (-3, 4) on a coordinate plane.
2. Find the distance between the points (1, 3) and (5, 7).
3. Find the midpoint between the points (-2, 6) and (4, -2).

Remember to always label your axes and units when graphing points and solving problems with rectangular coordinates.

Now that you've learned about rectangular coordinates, you can practice graphing points, finding distances, and calculating midpoints to strengthen your understanding of this topic.

Good luck with your studies!