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Nov 29, 2025

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1 page

Understanding the Pythagorean Theorem

Medha Karnati

@medhakarnati_yhhb

The coordinate geometry unit covers essential concepts for navigating the... Show more

$Unit 1: Lesson 1.1. -axis II I Sorigin →x-axis III IV Unit 1: Lesson2 Pythagorean Theorem: a² + b² = c2 1 Distence Formula: d=$\sqrt{$

Coordinate Geometry Fundamentals

The coordinate plane is divided into four quadrants (I, II, III, IV) by the x-axis and y-axis, which intersect at the origin. This system gives us a way to pinpoint exact locations using ordered pairs (x,y).

The Pythagorean Theorem $a² + b² = c²$ is the foundation for the distance formula, which lets you find the distance between any two points: d = √ $(x₂-x₁)² + (y₂-y₁)²$ . When you need to find the midpoint between two locations, use the midpoint formula: $[(x₁+x₂)/2], [(y₁+y₂)/2]$ - just average the x-coordinates and y-coordinates.

When sketching graphs, follow these steps: isolate a variable when possible, create a table of values, plot the points, and connect them with a smooth curve or line. You can identify symmetry in three ways: x-axis symmetry $x,-y$ , y-axis symmetry $-x,y$ , or origin symmetry $-x,-y$ .

Pro Tip: Test for symmetry algebraically by substituting -y for y $x-axis symmetry$ , -x for x $y-axis symmetry$ , or both -x and -y (origin symmetry). If you get an equivalent equation, symmetry exists!

The standard form of a circle equation is $x-h$ ² + $y-k$ ² = r², where (h,k) is the center and r is the radius. When the center is at the origin, this simplifies to x² + y² = r². This formula comes directly from applying the distance formula from the center to any point on the circle.

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Pre-Calculus

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Nov 29, 2025

•

1 page

Understanding the Pythagorean Theorem

Medha Karnati

@medhakarnati_yhhb

The coordinate geometry unit covers essential concepts for navigating the xy-plane and understanding geometric relationships. You'll learn about the coordinate system, distance calculations, and how to analyze and graph equations with precision.

$Unit 1: Lesson 1.1. -axis II I Sorigin →x-axis III IV Unit 1: Lesson2 Pythagorean Theorem: a² + b² = c2 1 Distence Formula: d=$\sqrt{$

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Coordinate Geometry Fundamentals

Pro Tip: Test for symmetry algebraically by substituting -y for y $x-axis symmetry$ , -x for x $y-axis symmetry$ , or both -x and -y (origin symmetry). If you get an equivalent equation, symmetry exists!