Mathematics
Grade 6
15 min
Follow directions on a coordinate plane
Follow directions on a coordinate plane
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1
Introduction & Learning Objectives
Learning Objectives
Identify the x-axis, y-axis, and origin on a coordinate plane.
Accurately plot given ordered pairs (x, y) on a coordinate plane.
Interpret directional instructions (right, left, up, down) in relation to the coordinate plane.
Determine the new coordinates of a point after a series of directional movements.
Locate a point on the coordinate plane by following a sequence of steps from a starting point.
Describe the movement required to get from one point to another using directional language.
Ever tried to give someone directions to a hidden treasure? 🗺️ It's much easier when you have a map and clear instructions!
In this lesson, you'll learn how to use a special kind of map called a coordinate plane to follow directions and find exact locations. U...
2
Key Concepts & Vocabulary
TermDefinitionExample
Coordinate PlaneA two-dimensional surface formed by the intersection of two perpendicular number lines, used to locate points.A graph paper grid is a visual representation of a coordinate plane.
OriginThe central point where the x-axis and y-axis intersect on a coordinate plane, represented by the ordered pair (0, 0).If you start at (0,0) and move 3 units right, you are moving from the origin.
x-axisThe horizontal number line on the coordinate plane, used to measure horizontal distance from the origin.In the point (5, 2), the '5' tells you to move 5 units along the x-axis.
y-axisThe vertical number line on the coordinate plane, used to measure vertical distance from the origin.In the point (5, 2), the '2' tells you to move 2 units along the y-axis...
3
Core Formulas
Plotting an Ordered Pair (x, y)
Start at the origin (0, 0). Move horizontally along the x-axis according to the x-coordinate (right for positive, left for negative). Then, move vertically parallel to the y-axis according to the y-coordinate (up for positive, down for negative).
This rule tells you how to place any point on the coordinate plane using its unique address. Always move horizontally first, then vertically.
Horizontal Movement (Right/Left)
To move 'R' units right, add R to the x-coordinate: $(x, y) \rightarrow (x+R, y)$. To move 'L' units left, subtract L from the x-coordinate: $(x, y) \rightarrow (x-L, y)$.
This rule explains how horizontal movements change only the x-coordinate of a point. The y-coordinate remains unchanged during horizontal m...
5 more steps in this tutorial
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Challenging
Three corners of a rectangle are located at A(2, 2), B(7, 2), and C(7, 6). To find the fourth corner, D, you must follow the same directional movement from A as the movement from B to C. What are the coordinates of corner D?
A.(2, 6)
B.(7, -2)
C.(2, 7)
D.(6, 2)
Challenging
Start at point (2, 1). Move right a number of units equal to (12 / 4). Then move up a number of units equal to (3 * 2). What is your final position?
A.(6, 8)
B.(5, 7)
C.(3, 6)
D.(14, 7)
Challenging
A treasure map has instructions: 'Start at the old well (3, 3). Go 6 units east (right), then 4 units north (up). From there, go 2 units west (left), and finally 1 unit north (up).' Where is the treasure buried?
A.(7, 8)
B.(5, 8)
C.(7, 7)
D.(11, 8)
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