Write the gradient of the line perpendicular to the line with gradient.
(a) 5 , (b) 7 , (c) -4 , (d) -9 , (e) 1/2 , (f) -3/4 , (g) 3/8 , (h) -2/3
Thank you John
To find the gradient of a line perpendicular to a line with a given gradient, we need to take the negative reciprocal of the given gradient.
Let's calculate the gradients for each given option:
(a) The gradient of the line perpendicular to a line with a gradient of 5 would be -1/5.
(b) The gradient of the line perpendicular to a line with a gradient of 7 would be -1/7.
(c) The gradient of the line perpendicular to a line with a gradient of -4 would be 1/4.
(d) The gradient of the line perpendicular to a line with a gradient of -9 would be 1/9.
(e) The gradient of the line perpendicular to a line with a gradient of 1/2 would be -2.
(f) The gradient of the line perpendicular to a line with a gradient of -3/4 would be 4/3.
(g) The gradient of the line perpendicular to a line with a gradient of 3/8 would be -8/3.
(h) The gradient of the line perpendicular to a line with a gradient of -2/3 would be 3/2.
So, the gradients of the lines perpendicular to the given options are:
(a) -1/5
(b) -1/7
(c) 1/4
(d) 1/9
(e) -2
(f) 4/3
(g) -8/3
(h) 3/2
To find the gradient of a line perpendicular to another line with a given gradient, you need to take the negative reciprocal of the given gradient.
Let's go through each option one by one:
(a) The gradient of the line perpendicular to a line with a gradient of 5 would be -1/5.
(b) The gradient of the line perpendicular to a line with a gradient of 7 would be -1/7.
(c) The gradient of the line perpendicular to a line with a gradient of -4 would be 1/4.
(d) The gradient of the line perpendicular to a line with a gradient of -9 would be 1/9.
(e) The gradient of the line perpendicular to a line with a gradient of 1/2 would be -2.
(f) The gradient of the line perpendicular to a line with a gradient of -3/4 would be 4/3.
(g) The gradient of the line perpendicular to a line with a gradient of 3/8 would be -8/3.
(h) The gradient of the line perpendicular to a line with a gradient of -2/3 would be 3/2.
Therefore, the correct answers are:
(a) -1/5
(b) -1/7
(c) 1/4
(d) 1/9
(e) -2
(f) 4/3
(g) -8/3
(h) 3/2
If two lines are perpendicular their slopes or gradients are negative reciprocals of each other:
5 -1/5
-4 1/4
1/2 -2
do you see the idea?
Also the two gradients will multiply to equal -1. You can use that as a check.