<h3>The Cartesian plane</h3><p>The <strong>Cartesian plane</strong> has an x-axis (horizontal) and a y-axis (vertical) crossing at the <strong>origin</strong> (0, 0). A point is written as <code>(x, y)</code>, x first.</p><h3>Distance between points</h3><p>The <strong>distance</strong> between (x1, y1) and (x2, y2) is <code>d = √((x2 - x1)² + (y2 - y1)²)</code>. Between (1, 2) and (4, 6) it is <code>√(3² + 4²) = √25 = 5</code>.</p><h3>Midpoint</h3><p>The <strong>midpoint</strong> is the average of the coordinates: <code>M = ((x1 + x2)/2, (y1 + y2)/2)</code>. The midpoint of (2, 4) and (6, 8) is (4, 6).</p><div class="callout"><strong>Kenyan context:</strong> On a town grid, a school is at point (2, 3) and a market at (8, 11), where each unit is 100 m. The straight-line distance is <code>√((8-2)² + (11-3)²) = √(36 + 64) = √100 = 10</code> units, that is 1000 m apart. A water point built halfway sits at the midpoint (5, 7).</div>