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This Lesson (Find the equation of a perpendicular line through a given point) was created by by math_tutor2020(3816)
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This lesson will go over an example problem detailing how to find the equation of a perpendicular line through a given point.
Problem: Consider the equation 3x-7y = 19 Find the equation of the perpendicular line through (0.5, -2.5) ----------------- Solution: The given equation is of the form Ax+By = C Anything perpendicular to this is of the form Bx-Ay = D We have the A,B values swap places. Also, the new y coefficient becomes negated. The given equation has A = 3 and B = -7, so Bx-Ay = D updates to -7x-3y = D Then we'll plug in the coordinates of (0.5, -2.5) to determine the value of D. -7x-3y = D -7(0.5)-3(-2.5) = D -3.5+7.5 = D 4 = D D = 4 Therefore, we go from -7x-3y = D to -7x-3y = 4 as the final answer. ----------------------- Check: To confirm that 3x-7y = 19 is perpendicular to -7x-3y = 4, find the slope of each Recall that Ax+By = C has a slope of m = -A/B. This means 3x-7y = 19 has a slope of m = -3/(-7) = 3/7 Meanwhile -7x-3y = 4 has a slope of m = -(-7)/(-3) = -7/3 Then note how the slopes multiply to -1 (3/7)*(-7/3) = -1 This property of multiplying to -1 works for any pair of perpendicular slopes (proof shown here). This is as long as neither line is vertical nor horizontal. Graph: 3x-7y = 19 is in green -7x-3y = 4 is in blue These two lines form a 90 degree angle when meeting up. You can use graphing tools like Desmos, GeoGebra, or anything similar to help confirm the answer. This lesson has been accessed 1346 times. |
