Cartesian Coordinates

Cartesian coordinates are a system of locating points on a plane using two perpendicular number lines, called the x-axis and y-axis. The point where the axes intersect is called the origin, denoted by the coordinates (0, 0).

Parts of Cartesian Coordinates

X-Axis: The horizontal number line. Points to the right of the origin have positive x-coordinates, and points to the left have negative x-coordinates.

Y-Axis: The vertical number line. Points above the origin have positive y-coordinates, and points below have negative y-coordinates.

Quadrants: The plane is divided into four quadrants, labeled I, II, III, and IV, going counterclockwise from the upper right quadrant.

Coordinates of a Point

On a Cartesian plane, each point has a unique pair of coordinates (x, y), where x is the distance along the x-axis, and y is the distance along the y-axis.

Distance Formula

The distance between two points with coordinates (x1, y1) and (x2, y2) can be found using the distance formula:
√((x2 - x1)^2 + (y2 - y1)^2).

Practice Problems

Plot the points A(3, 4), B(-2, 5), C(-1, -3), and D(2, -6) on a Cartesian plane.
Find the distance between the points (1, 2) and (-3, 5).

Answer to Practice Problems

Answer:
A(3, 4) is in quadrant I, B(-2, 5) is in quadrant II, C(-1, -3) is in quadrant III, and D(2, -6) is in quadrant IV.
Answer:
The distance between the points (1, 2) and (-3, 5) is √(((-3) - 1)^2 + (5 - 2)^2) = √((-4)^2 + (3)^2) = √(16 + 9) = √25 = 5 units.

◂Math Worksheets and Study Guides Sixth Grade. Algebraic Equations

The resources above cover the following skills:

Algebra (NCTM)

Represent and analyze mathematical situations and structures using algebraic symbols.

Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations

Grade 6 Curriculum Focal Points (NCTM)

Algebra: Writing, interpreting, and using mathematical expressions and equations

Students write mathematical expressions and equations that correspond to given situations, they evaluate expressions, and they use expressions and formulas to solve problems. They understand that variables represent numbers whose exact values are not yet specified, and they use variables appropriately. Students understand that expressions in different forms can be equivalent, and they can rewrite an expression to represent a quantity in a different way (e.g., to make it more compact or to feature different information). Students know that the solutions of an equation are the values of the variables that make the equation true. They solve simple one-step equations by using number sense, properties of operations, and the idea of maintaining equality on both sides of an equation. They construct and analyze tables (e.g., to show quantities that are in equivalent ratios), and they use equations to describe simple relationships (such as 3x = y) shown in a table.