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find the gradient of a line pe

rpendicular to the line joining these pairs of points
(a) (1,2) and (5,-6)
(b) (2,4) and (3,8)
(c) (-2,1) and (2,-4)

perpendicular lines have slopes which are negative reciprocals. So,

(a) slope = (-6-2)/(5-1) = -2 so ⊥ slope is 1/2
do the others in like wise

Did you know?

Did you know that finding the gradient of a line perpendicular to the line joining two points can be determined by taking the negative reciprocal of the original line's gradient? For example, if we have the points (1,2) and (5,-6), the original line's gradient is calculated as (change in y / change in x) = (-6 - 2) / (5 - 1) = -2. Therefore, the gradient of the line perpendicular to this line would be the negative reciprocal, resulting in -1 / -2 = 1/2. Similarly, we can apply this method to find the gradients of lines perpendicular to the line joining the points (2,4) and (3,8), which gives us the original line's gradient as (8 - 4) / (3 - 2) = 4. Therefore, the gradient of the line perpendicular to this line would be -1 / 4. Lastly, for the points (-2,1) and (2,-4), the original line's gradient is calculated as (-4 - 1) / (2 - (-2)) = -1/2. Thus, the gradient of the line perpendicular to this line would be 2.