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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Coordinate Geometry</title>
<style>
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</style>
</head>
<body>
<header>
Coordinate Geometry
</header>
<section>
<h1>Coordinate Geometry Overview</h1>
<p>Coordinate geometry, also known as analytic geometry, is the study of geometry using a coordinate system. It involves using algebraic methods to solve geometric problems. The central idea is to represent geometric shapes, points, and objects in a coordinate plane (usually Cartesian coordinates) and to apply algebraic techniques to analyze and solve geometric problems.</p>
<p>In coordinate geometry, every point in the plane is represented by an ordered pair of numbers <code>(x, y)</code>, where <code>x</code> is the horizontal coordinate and <code>y</code> is the vertical coordinate.</p>
<h2 class="section-header">Key Concepts:</h2>
<ul>
<li><strong>Coordinate Plane:</strong> The coordinate plane consists of two perpendicular axes: the <code>x</code>-axis (horizontal) and the <code>y</code>-axis (vertical). The point where the two axes intersect is the <strong>origin</strong>, denoted by <code>(0, 0)</code>.</li>
<li>The plane is divided into four quadrants:
<ul>
<li>Quadrant I: <code>x > 0</code> and <code>y > 0</code></li>
<li>Quadrant II: <code>x < 0</code> and <code>y > 0</code></li>
<li>Quadrant III: <code>x < 0</code> and <code>y < 0</code></li>
<li>Quadrant IV: <code>x > 0</code> and <code>y < 0</code></li>
</ul>
</li>
</ul>
<h2 class="section-header">Important Formulas:</h2>
<div class="math-box">
<p class="formula">1. Distance Formula: <br>
<code>d = √((x₂ - x₁)² + (y₂ - y₁)²)</code></p>
<p class="formula">2. Midpoint Formula: <br>
<code>M = ((x₁ + x₂)/2, (y₁ + y₂)/2)</code></p>
<p class="formula">3. Slope Formula: <br>
<code>m = (y₂ - y₁) / (x₂ - x₁)</code></p>
<p class="formula">4. Equation of a Line (Point-Slope Form): <br>
<code>y - y₁ = m(x - x₁)</code></p>
<p class="formula">5. Equation of a Line (Slope-Intercept Form): <br>
<code>y = mx + b</code></p>
<p class="formula">6. Equation of a Line (General Form): <br>
<code>Ax + By + C = 0</code></p>
<p class="formula">7. Circle Equation: <br>
<code>(x - h)² + (y - k)² = r²</code></p>
</div>
<h2 class="section-header">Example Problems:</h2>
<div class="example">
<p><strong>1. Distance Between Two Points:</strong></p>
<p>Find the distance between points A(2, 3) and B(5, 7).</p>
<p>Using the distance formula: <br>
<code>d = √((5 - 2)² + (7 - 3)²) = √(3² + 4²) = √(9 + 16) = √25 = 5</code></p>
<p>Therefore, the distance between A and B is 5 units.</p>
</div>
<div class="example">
<p><strong>2. Midpoint of Two Points:</strong></p>
<p>Find the midpoint of points A(2, 3) and B(5, 7).</p>
<p>Using the midpoint formula: <br>
<code>M = ((2 + 5)/2, (3 + 7)/2) = (7/2, 10/2) = (3.5, 5)</code></p>
<p>Therefore, the midpoint of A and B is (3.5, 5).</p>
</div>
<div class="example">
<p><strong>3. Equation of a Line:</strong></p>
<p>Find the equation of the line passing through the points A(1, 2) and B(3, 6).</p>
<p>First, find the slope using the slope formula: <br>
<code>m = (6 - 2) / (3 - 1) = 4 / 2 = 2</code></p>
<p>Now, using the point-slope form, the equation of the line is: <br>
<code>y - 2 = 2(x - 1)</code> <br>
Simplifying: <br>
<code>y - 2 = 2x - 2 → y = 2x</code></p>
<p>Therefore, the equation of the line is <code>y = 2x</code>.</p>
</div>
</section>
<footer>
© 2025 Yoseph Feyisa Wegi | All Rights Reserved.
</footer>
</body>
</html>