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Katyanochek1 [597]
3 years ago
6

. If a pair of parallel lines are rotated, which is true?

Mathematics
2 answers:
kykrilka [37]3 years ago
7 0

Answer:  The correct option is (C)  Rotated parallel lines always remain parallel lines.

Step-by-step explanation:  We are given ton select the correct statement about the rotation of two parallel lines.

We know that two parallel lines have same slope.

So, let m = 2 be the slope of the two parallel lines and 4, 7 are the y-intercepts.

Then, the equations of the lines are given by

y=2x+4~~~~~~~~~~~~~~~~~~~~(i)\\y=2x+7~~~~~~~~~~~~~~~~~~~~(ii)

Let us rotate the lines through an angle of 90° clockwise.

The co-ordinates of the point (x, y), after rotating 90° clockwise becomes (y, -x).

We have

P(-1, 2) and Q(1, 6) are two points on the line (i) and R(-1, 5) and S(1, 9) are two points on the line (ii).

So, after rotation, they become

P(-1, 2)  ⇒  P'(2, 1),

Q(1, 6) ⇒  Q'(6, -1),

R(-1, 5)  ⇒  R'(5, 1),

S(1, 9)  ⇒  S'(9, -1).

So, slope of line (i) is

m_1=\dfrac{-1-1}{6-2}=-\dfrac{1}{2},

and the slope of line (ii) is

m_2=\dfrac{-1-1}{9-5}=-\dfrac{1}{2}.

Since, m_1=m_2,

so the slopes of the lines after rotation is again same, and hence they are again parallel to each other.

So, the angle of rotation (90° or 180° or 360°)does not matter, the parallel lines will always be parallel.

Thus, the rotated parallel lines always remain parallel lines.

Option (C) is correct.

shutvik [7]3 years ago
6 0
C.
Rotating parallel lines by the same amount does not change their parallel nature.
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Step-by-step explanation:

hi

personally this is how i would do this question but there are other ways.

i would start off by seeing how many sundays there are in the month (which is 5) then the number of other days which is 25. i'd then multiply 5 by 510 which is 2550. add that to 240 times 25 (which is 6000) and all of that together is 8550. divide that by the number of the days in the month (30) and then you'll get the daily avergae for the month

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