Straight-line explorer

<p>Read a coordinate pair in the order horizontal position, then vertical position. Use the same point order in both differences when calculating a gradient.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="width: 100%;"><thead><tr><th style="text-align: center; --cell-justify: center">Quantity</th><th style="text-align: center; --cell-justify: center">Calculation</th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">Gradient of \(AB\)</td><td style="text-align: center; --cell-justify: center">\(m=\dfrac{y_B-y_A}{x_B-x_A}\), provided \(x_B\ne x_A\)</td></tr><tr><td style="text-align: center; --cell-justify: center">Length of \(AB\)</td><td style="text-align: center; --cell-justify: center">\(AB=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\)</td></tr></tbody></table></div></div>
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<p>A rising line has positive gradient; a falling line has negative gradient. A horizontal line has gradient \(0\). A vertical line has no defined gradient because its horizontal change is zero.</p>
<p>Distance is always nonnegative. Gradient is a signed ratio, so a negative gradient does not mean a negative distance.</p>

Read a coordinate pair in the order horizontal position, then vertical position. Use the same point order in both differences when calculating a gradient.

A rising line has positive gradient; a falling line has negative gradient. A horizontal line has gradient \(0\). A vertical line has no defined gradient because its horizontal change is zero.

Distance is always nonnegative. Gradient is a signed ratio, so a negative gradient does not mean a negative distance.

Gradient and distance

Gradient and distance

Quantity	Calculation
Gradient of \(AB\)	\(m=\dfrac{y_B-y_A}{x_B-x_A}\), provided \(x_B\ne x_A\)
Length of \(AB\)	\(AB=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\)