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Questo esame si sostiene in inglese: le lezioni e le domande sono in inglese. L'interfaccia resta in italiano.
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Part 1 of 1
The slope of a line passing through (x_1, y_1) and (x_2, y_2) is m = (y_2 - y_1) / (x_2 - x_1). The slope-intercept form is y = mx + c. Parallel lines share equal slopes (m_1 = m_2). Perpendicular lines have negative reciprocal slopes (m_1 * m_2 = -1).
Distance formula: d = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2). Midpoint formula: M = ((x_1 + x_2)/2, (y_1 + y_2)/2).
Worked example
Find the equation of the line passing through (2, 5) perpendicular to y = 3x - 1. Original slope m = 3. Perpendicular slope m_perp = -1/3. Point-slope form: y - 5 = (-1/3)(x - 2) implies 3y - 15 = -x + 2, giving line equation x + 3y - 17 = 0.
1.Two non-vertical lines are perpendicular if and only if the product of their slopes equals -1.
2.The distance between (0, 0) and (3, 4) is 7.
3.The midpoint between (-2, 4) and (6, 8) is (2, 6).
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