Mathematics
Grade 7
15 min
Coordinate plane review
Coordinate plane review
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify and label the x-axis, y-axis, origin, and four quadrants of the coordinate plane.
Accurately plot ordered pairs (x, y) in all four quadrants and on the axes.
Read and write the coordinates of a given point on the coordinate plane.
Determine the quadrant in which a point lies based on the signs of its coordinates.
Understand the meaning of positive and negative coordinates in relation to the origin.
Recognize real-world situations where the coordinate plane is used.
Ever wonder how a pilot knows exactly where to fly, or how a video game character moves across the screen? 🎮 It's all thanks to a system called the coordinate plane!
In this lesson, we'll review the fundamental concepts of the coordinate plane, including its key components,...
2
Key Concepts & Vocabulary
TermDefinitionExample
Coordinate PlaneA two-dimensional surface formed by the intersection of two perpendicular number lines, used to locate points.Imagine a grid on a map where you can pinpoint any specific address.
x-axisThe horizontal number line on the coordinate plane.When you move left or right from the center, you are moving along the x-axis.
y-axisThe vertical number line on the coordinate plane.When you move up or down from the center, you are moving along the y-axis.
OriginThe point where the x-axis and y-axis intersect, represented by the ordered pair (0, 0).The exact center of the coordinate plane, like the starting point of a treasure hunt.
Ordered PairA pair of numbers (x, y) that specifies the location of a point on the coordinate plane, where 'x' is the horizonta...
3
Core Formulas
Ordered Pair Notation
$(x, y)$
Always write the x-coordinate first, followed by the y-coordinate, enclosed in parentheses. The x-coordinate tells you how far to move horizontally (left/right), and the y-coordinate tells you how far to move vertically (up/down).
Origin Coordinates
$(0, 0)$
The origin is the starting point for plotting all other points. It has an x-coordinate of 0 and a y-coordinate of 0.
Quadrant Signs
Quadrant I: $(+, +)$
Quadrant II: $(−, +)$
Quadrant III: $(−, −)$
Quadrant IV: $(+, −)$
The signs of the x and y coordinates determine which quadrant a point lies in. Points on the axes (where x=0 or y=0) are not considered to be in any quadrant.
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Challenging
A rectangle has vertices at A(-4, 3), B(2, 3), and C(2, -1). What are the coordinates of the fourth vertex, D, needed to complete the rectangle?
A.(-4, -1)
B.(-4, 2)
C.(3, -1)
D.(-1, -4)
Challenging
A point (a, b) is located in Quadrant I. If this point is reflected across the x-axis, what will be the signs of the coordinates of the new point?
A.(-, +)
B.(-, -)
C.(+, +)
D.(+, -)
Challenging
A student follows these instructions: 'Start at the origin, move 4 units right, then 2 units up. From there, move 6 units left, then 5 units down.' The student makes a mistake and starts at (1, 1) instead of the origin. What are the coordinates of their final, incorrect position?
A.(-2, -3)
B.(-1, -2)
C.(11, 8)
D.(-5, -4)
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