Question

2 Find the gradient of a line which is
perpendicular to each of the following lines:
a y=-3x+11
b
*+2y=0
4
c y=-3
d y=
2(x-1)
3
6 A straight connecting street segment is
built perpendicular to an existing street
2
with equation y=x+3. Determine the
equation of the line of the new street
segment, which passes through point
B(-1,-0.2).
7 A fish farm builds a breeding basin in the
form of a quadrilateral ABCD, with
A(-3,-1), B(2,0), C(5,3) and D(0,2).
Show that the quadrilateral ABCD is a
parallelogram.

Answer 1

We get the gradient of the lines which is perpendicular to the given lines as 1/3, -8, 0 and -3/2.

We are given some equation of the lines and we need to find the gradient of the lines which are perpendicular to them.

For this, we will first find the slope of the lines and then reciprocal it and change their signs to obtain the gradient of the perpendicular lines.

a) y = -3 x + 11

Here we can see that the slope of the line is:

m = -3

So, the gradient of the perpendicular line will be:

m' = 1 / 3

b) - x / 4 + 2 y = 0

2 y = x / 4

y = x / 8

slope = m = 1 / 8

Gradient = m' = - 8

c) y = - 3

Slope = m = 0

Gradient = m' = 0

d) y = 2(x - 1) / 3

y = 2/3 x - 1/3

slope = m = 2/3

Gradient = m' = -3/2.

Therefore, we get the gradient of the lines which is perpendicular to the given lines as 1/3, -8, 0 and -3/2.

Learn more about gradients here:

https://brainly.com/question/21727173

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