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Distance and midpoint

$d = \sqrt{\Delta x^2 + \Delta y^2}$ ; midpoint = average of the coordinates.

Watch out: average, not half the difference.

Parallel and perpendicular slopes

Parallel: equal. Perpendicular: $m_1 m_2 = -1$ .

Watch out: flip and change the sign.

Equations of lines

$y = y_1 + m(x - x_1)$ ; find $b$ by substituting the point.

Watch out: parallel lines share the slope, not the intercept.

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