# Perpendicular line gradient (higher gcse)Watch

Thread starter 1 year ago
#1
Not understanding what to do exactly.

The question is:
Line A and B are perpendicular and intersect at (3, 3). If line A has the equation 3y - x = 6, what is the equation of line B ?

Don't say anything about defferentiation please as we down learn that at gcse and I just don't understand that.

(Although if you could explain defferentiation to me also it would be helpful)
0
1 year ago
#2
you need to rearrange the first equation into the form y = mx + c

from this you can predict the gradient of the other line...

for instance if m = 2/3 the other m = -3/2

if m = -8 the other m = 1/8
3
1 year ago
#3
Well if line A is perpendicuar to Line B: Then the gradients are the negative reciprocals of each other and multiply to give -1.
Rearrange the equation for line A to get your gradient.
The using your gradient from line A find the negative reciprocal.
Substitue this into the equation:
Y-y1=m(x-x1) to get line B
1
1 year ago
#4
Differentiating for linear graphs isn't entirely useful, although it may be useful for normals to curves, for example line A and B being normals to a quadratic curve. In this situation you would differentiate the quadratic curve, and then subsitute the x coordinates of the two given points, through this you would obtain the gradient of the tangents to which the normals touch. Using the negative reciprocal it is then possible to calculate the gradient of the two normals, A and B, and hence using the above equation, as stated previously, can be used to work out the equations of the two normals.
0
Thread starter 1 year ago
#5
(Original post by Science99999)
Differentiating for linear graphs isn't entirely useful, although it may be useful for normals to curves, for example line A and B being normals to a quadratic curve. In this situation you would differentiate the quadratic curve, and then subsitute the x coordinates of the two given points, through this you would obtain the gradient of the tangents to which the normals touch. Using the negative reciprocal it is then possible to calculate the gradient of the two normals, A and B, and hence using the above equation, as stated previously, can be used to work out the equations of the two normals.
Oh so how do you defferentiate the quadratic curve
0
1 year ago
#6
(Original post by Walker16)
Oh so how do you defferentiate the quadratic curve
Differentiation is not needed for this question. Don't bother learning it for GCSE. You will learn about differentiation if you choose maths for A-level.

For this question, rearrange the equation of line A in the form y = mx + c to find its gradient.
From that, you can work out the gradient of line B (do you know what the link is between the gradient of perpendicular lines?).

Once you have found the gradient, you can find the equation of line B by using y1 = mx1 + c to find what c is.
Alternatively, you could use the formula y - y1 = m(x - x1) to work out the equation.
(x1,y1) - coordinates through which the line passes
m - gradient of the line.

Hope that helps!
0
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