How Do You Find Perpendicular Lines?


Quick Answer

Perpendicular lines are lines that intersect one another at a 90 degree angle. If two lines are perpendicular, then multiplying the slopes of the two lines together equals -1.

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Full Answer

To demonstrate this, suppose you are given the following formulas for lines: y1 = -2x + 6 and y2 = 0.5x + 3. The first step in determining whether the given lines are perpendicular is to decide the slope of each line. Using the formula for a line, y = mx + b, where the value of m is the slope of the line, for the two lines given above, the slopes are -2 for y1 and 0.5 for y2. The second step is to multiply the two slopes together. Multiplying -2 and 0.5 gives -1, which indicates that the two lines are perpendicular.

More generally, if m1 and m2 represent the slopes of two separate lines, in any case where m1*m2 = -1, the lines are perpendicular. Rearranging this formula also shows that m1 = -1/m2 and that m2 = -1/m1 for any set of perpendicular lines. Given the details of one line, it is therefore possible to find the slope of the one perpendicular to it using these formulas. For instance, if asked to find the slope of a line perpendicular to y = -2x + 6, plug -2 into the appropriate formula to give m2 = -1/-2. This equals 0.5, as seen in the first example for y2.

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