# 6.8 - Coordinate Graphing

6.8  The student will

a)  identify the components of the coordinate plane; and

b)  identify the coordinates of a point and graph ordered pairs in a coordinate plane.

### BIG IDEAS

• I can find specific locations on a grid or map.
• I will understand that an ordered pair represents a unique location in space.

### UNDERSTANDING THE STANDARD

2016 VDOE Curriculum Framework - 6.8 Understanding

·  In a coordinate plane, the coordinates of a point are typically represented by the ordered pair (x, y), where x is the first coordinate and y is the second coordinate.

·  Any given point is defined by only one ordered pair in the coordinate plane.

·  The grid lines on a coordinate plane are perpendicular.

·  The axes of the coordinate plane are the two intersecting perpendicular lines that divide it into its four quadrants. The x-axis is the horizontal axis and the y-axis is the vertical axis.

·  The quadrants of a coordinate plane are the four regions created by the two intersecting perpendicular lines (x- and y-axes). Quadrants are named in counterclockwise order. The signs on the ordered pairs for quadrant I are (+,+); for quadrant II, (–,+); for quadrant III, (–, –); and for quadrant IV, (+,–).

·  In a coordinate plane, the origin is the point at the intersection of the x-axis and y-axis; the coordinates of this point are (0, 0).

·  For all points on the x-axis, the y-coordinate is 0.  For all points on the y-axis, the x-coordinate is 0.

·  The coordinates may be used to name the point. (e.g., the point (2, 7)). It is not necessary to say
“the point whose coordinates are(2, 7).” The first coordinate tells the location or distance of the point to the left or right of the y-axis and the second coordinate tells the location or distance of the point above or below the x-axis. For example, (2, 7) is two units to the right of the y-axis and seven units above the x-axis.

·  Coordinates of points having the same x-coordinate are located on the same vertical line. For example, (2, 4) and (2, -3) are both two units to the right of the y-axis and are vertically seven units from each other.

·  Coordinates of points having the same y-coordinate are located on the same horizontal line. For example, (-4, -2) and (2, -2) are both two units below the x-axis and are horizontally six units from each other.

### ESSENTIALS

• Can any given point be represented by more than one ordered pair?
The coordinates of a point define its unique location in a coordinate plane. Any given point is defined by only one ordered pair.
• In naming a point in the plane, does the order of the two coordinates matter?
Yes. The first coordinate tells the location of the point to the left or right of the y-axis and the second point tells the location of the point above or below the x-axis. Point (0, 0) is at the origin.

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

·  6.8a1  Identify and label the axes, origin, and quadrants of a coordinate plane.

·  6.8a2  Identify the quadrant or the axis on which a point is positioned by examining the coordinates (ordered pair) of the point. Ordered pairs will be limited to coordinates expressed as integers.

·  6.8b2  Identify ordered pairs represented by points in the four quadrants and on the axes of the coordinate plane. Ordered pairs will be limited to coordinates expressed as integers.

·  6.8b3  Relate the coordinates of a point to the distance from each axis and relate the coordinates of a single point to another point on the same horizontal or vertical line. Ordered pairs will be limited to coordinates expressed as integers.

·  6.8b1  Graph ordered pairs in the four quadrants and on the axes of a coordinate plane. Ordered pairs will be limited to coordinates expressed as integers.

·  6.8b4  Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to determine the length of a side joining points with the same first coordinate or the same second coordinate. Ordered pairs will be limited to coordinates expressed as integers. Apply these techniques in the context of solving practical and mathematical problems.

### KEY VOCABULARY

coordinate plane, ordered pair, quadrant, perpendicular, counterclockwise, origin, x-axis, y-axis, location, intersection, intersecting lines, horizontal, vertical, graph

Updated: Nov 20, 2018