Free ebook on coordinate geometry: plot points, find distance, midpoint and slope, write line equations, and verify shapes on the plane.
Free ebook content
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Coordinate Geometry Basics: Understanding the Coordinate Plane
+ Exercise: Using the “x then y” rule, which directions correctly plot the point (-4, 6) from the origin?
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Coordinate Geometry Basics: Plotting Points and Reading Graphs
+ Exercise: When plotting a point (x, y) on a coordinate plane, which routine best helps avoid common direction mistakes?
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Coordinate Geometry Basics: Horizontal and Vertical Movement on the Plane
+ Exercise: Which statement correctly explains why the segment from (-5, 0) to (1, 3) is neither horizontal nor vertical, and why its length is not found by a single absolute difference?
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Coordinate Geometry Basics: Distance Between Two Points
+ Exercise: Why are the coordinate differences (x2 − x1) and (y2 − y1) squared in the distance formula?
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Coordinate Geometry Basics: Midpoint of a Segment and Coordinate Averages
+ Exercise: Given endpoint A(1, 3) and midpoint M(4, -1) of segment AB, what are the coordinates of endpoint B?
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Coordinate Geometry Basics: Slope as Rate of Change and Steepness
+ Exercise: Two segments have slopes m = 2 and m = -2. Which statement best compares their steepness?
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Coordinate Geometry Basics: Equations of Lines from Points and Slope
+ Exercise: A line passes through (0, -2) and (4, 6). What is its equation in slope-intercept form y = mx + b?
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Coordinate Geometry Basics: Analyzing Triangles on the Coordinate Plane
+ Exercise: Given triangle PQR with P(-1,2), Q(3,2), and R(1,6), which conclusion is supported by comparing squared side lengths?
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Coordinate Geometry Basics: Rectangles and Parallelograms Using Slopes and Distances
+ Exercise: When checking whether four ordered points A→B→C→D form a rectangle, which set of conditions is sufficient using the distance-heavy method?
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Coordinate Geometry Basics: Coordinate-Based Proofs and Shape Verification
+ Exercise: When trying to prove that two diagonals bisect each other using coordinates, which computation is the most direct method?
About the free ebook
Coordinate Geometry Basics: Graphing Shapes on the Plane
Build confidence with coordinate geometry by learning how points, lines, and polygons work on a two-dimensional plane. This free ebook introduces the x-axis, y-axis, quadrants, ordered pairs, and the practical skills needed to interpret and create graphs accurately.
Turn coordinates into geometric evidence
Move beyond plotting individual points to analyze relationships between them. Practice finding horizontal and vertical changes, calculating distance and midpoint, and using slope to describe a line’s direction and steepness. Clear coordinate methods help make geometry measurable and verifiable.
Graph and verify common shapes
Use coordinates to investigate triangles, rectangles, and parallelograms. You will apply slopes to identify parallel or perpendicular sides and distances to test whether sides are congruent. The ebook also explains how coordinate-based proofs support conclusions about a shape.
Skills developed
- Plot and read ordered pairs on the coordinate plane.
- Calculate distance, midpoint, and slope from coordinates.
- Write equations of lines using points and slope.
- Classify and verify polygons with coordinate evidence.
Designed for school geometry study, this resource connects graphing skills with essential formulas and logical reasoning. Work through the examples and apply each method when solving coordinate-plane problems.
How do you find the distance between two points on a coordinate plane?
Subtract the x-coordinates and y-coordinates, square both differences, add them, and take the square root.
How can slopes prove that two sides of a shape are parallel or perpendicular?
Parallel lines have equal slopes. Perpendicular nonvertical lines have slopes whose product is -1.
What is the midpoint formula in coordinate geometry?
For endpoints (x1, y1) and (x2, y2), the midpoint is ((x1 + x2)/2, (y1 + y2)/2).
This ebook includes:
10 content chapters
Digital certificate of course completion (Free)
Exercises to train your knowledge
100% free, from content to certificate
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