Whoa! We have to get the opposite slope, so the line "stands up" more than it "lies down," but we also have to make it negative, so it goes downhill if the first line went uphill.Ī line where m = 1 2 is a positive slope (going uphill). It will be a reciprocal of the positive line's slope, BUT.Here is the difficult part of finding the slope of the line perpendicular to the positively sloping line: The two lines may not be oriented on a coordinate grid so that one of them lines up with (or is parallel to) either the x-axis or y-axis.
Perpendicular lines are lines intersecting at 90 °.
In plane geometry, negatives are found in slopes that go "downhill." How To Find Perpendicular Slope The negative of a negative number is a positive number.įor practice, find the negative values of: The negative of a positive number is a negative number. The reciprocal of 0.75 = 75 100 the reciprocal is 100 75 = 4 3.To find reciprocals of decimals, you can convert the decimal to a fraction and then find its reciprocal, or you can place the decimal under 1 as a fraction and use a calculator: To find reciprocals of whole numbers, place the number under 1 as a fraction: You can also find reciprocals of whole numbers and decimals. You may notice all you are doing with fractions is having the numerator and denominator switch places. Practice by finding reciprocals of these numbers: Reciprocals are two values such that multiplying them gives a product of 1, like 1 2 and 2 1:
Mathematically, it is the change in y-value compared to its change in x-value.Ī perpendicular slope is the negative reciprocal of any other slope. The slope of a line is its angle, or steepness, compared to that x-axis value. All slopes are compared to some other line, usually an x-axis. In plane geometry, all lines have slopes. A vertical line is perpendicular to a horizontal line. When two lines intersect at right angles, they are perpendicular lines, and we can measure their slope. When two lines intersect, they must do one of two things: intersect at right angles or intersect at other angles. © jumk.All pairs of lines in geometry must do one of two things: intersect or not intersect. These values then can be transferred increasing or decreasing to the upper calculator. Here, from two of these values, the third can be calculated. Often, only the total distance and the height are known. At a length of 200 feet, a height of 30 feet and a total distance of 202.24 feet is covered. When the slope is decreasing, height and slope have a minus as prefix.Įxample: a road with 15% slope has an angle of 8.53°. The distances in length and height and the total have the same unit (e.g. Or enter only the slope in degrees or percent to get the other value. The other two values and the total distance will be calculated. Please enter at distance and slope two values, of which at least one is a distance. JavaScript has to be enabled to use the calculator.Ĭalculate the slope in degrees and percent and the distances in length and height.