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Simora [160]
3 years ago
8

Find the distance between the pair of parallel lines.

Mathematics
2 answers:
Maurinko [17]3 years ago
6 0

Answer:

C) 3.58

Step-by-step explanation:

The distance between two parallel lines r1 and r2 is given by the absolute value of:

d(r_1,r_2)=\frac{ax_1+by_1+c}{\sqrt{a^{2}+b^{2}}}

Where a, b and c are the coefficients of the general form of the equation of the line r2 and x1 and y2 are the coordinates of one point that belongs to the line r1.

Let's call r1 the line define by: y = 2x +4 and r2 the line define by y=2x-4

So, the general form of the equation of line r2 is:

y = 2x - 4

0 = 2x - 4 - y

0 = 2x - y - 4

With this equation, a is equal to 2, b is equal to -1 and c is equal to -4.

Now, we need to found a point that belongs to line r1. This point can be found replacing x for any value and found y. If x is cero, for example, y is:

y = 2x +4

y = 2*0 + 4

y = 4

So, our point (x1, y1) is (0,4).

Replacing values of the equation of d(r1,r2), we get:

d(r_1,r_2)=\frac{(2*0)+(-1*4)+(-4)}{\sqrt{2^{2}+(-1)^{2}}}=

d(r_1,r_2)=\frac{-8}{\sqrt{5}} = -3.58

Then, the absolute value of -3.58 is 3.58, so the distance between the two parallel lines is 3.58.

guajiro [1.7K]3 years ago
6 0

Answer:

C) 3.58 is the correct answer.

Step-by-step explanation:

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Find the value of r so the line that passes through the pair of points has the given slope,
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6 0
2 years ago
Read 2 more answers
4
Helen [10]

Answer:

y-intercept is (0, -4)

x-intercept is (-5, 0)

Step-by-step explanation:

Remember the x-intercept and the y-intercept are the points on the graph where the line crosses the x-axis and the y-axis respectively.

We can find the x intercept and the y intercept a couple of ways. One way is to graph the line, which I will do later. The other way is to do a little math.

The equation of a line in y-intercept form is

y = mx + b

where b = the y-intercept

In our equation above and solving for y we get the y-intercept is -4

4x + 5y =  - 20 \\ 5y =  - 4x - 20 \\ y =  -  \frac{4}{5} x - 4

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6 0
3 years ago
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