ACT Preparation / Unit 9 ACT 0815 worked example, 60 to 90 seconds
The Perpendicular Line Through a Point
The idea
To write the line through a point perpendicular to a given line, work in three steps. First, put the given line in slope-intercept form and read its slope. Second, take the negative reciprocal. Third, use point-slope form with the new slope and the given point, then rearrange. For a parallel line, keep the same slope in the third step.
In practice
Worked example: the line through (4, 1) perpendicular to 2x − 3y = 6. Step one: −3y = −2x + 6, so y = (2/3)x − 2, with slope 2/3. Step two: the perpendicular slope is −3/2. Step three: y − 1 = −(3/2)(x − 4), so y = −(3/2)x + 7.
Where people slip
Read the slope only after solving for y. The coefficient of x in standard form is not the slope: here it is 2, while the slope is 2/3.
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