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The coordinates of four points are P(0, -3), Q(6, 1), R(-4, -4) and S(5, 2). Find out which line segments are parallel to each other.
  • a)
    PQ || RS 
  • b)
    PR || QR
  • c)
    (1) and (2) both
  • d)
    None of these 
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The coordinates of four points are P(0, -3), Q(6, 1), R(-4, -4) and S(...
Slope of PQ: [1 - (-3)]/[6 - 0] = 2/3 
Slope of RS: [2 - (-4)]/[5 - (-4)] = 2/3
Since the slopes of the two lines are equal, the lines are parallel. 
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Community Answer
The coordinates of four points are P(0, -3), Q(6, 1), R(-4, -4) and S(...
Given:
Coordinates of four points:
P(0, -3)
Q(6, 1)
R(-4, -4)
S(5, 2)

To find:
Which line segments are parallel to each other.

Solution:
1. Determining the slopes of the line segments:
The slope of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)

Calculating the slopes of the line segments:
- PQ: m(PQ) = (1 - (-3)) / (6 - 0) = 4 / 6 = 2/3
- QR: m(QR) = (-4 - 1) / (-4 - 6) = -5 / -10 = 1/2
- PR: m(PR) = (-4 - (-3)) / (-4 - 0) = -1 / -4 = 1/4
- RS: m(RS) = (2 - (-4)) / (5 - (-4)) = 6 / 9 = 2/3

2. Comparing the slopes:
- PQ and RS: The slopes of PQ (2/3) and RS (2/3) are equal. Therefore, PQ and RS are parallel. (Option a is correct)
- PR and QR: The slopes of PR (1/4) and QR (1/2) are not equal. Therefore, PR and QR are not parallel.
- None of the given line segments are parallel to each other. Therefore, option c is incorrect.

Conclusion:
The line segments PQ and RS are parallel to each other, as their slopes are equal. Therefore, the correct answer is option a) PQ || RS.
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The coordinates of four points are P(0, -3), Q(6, 1), R(-4, -4) and S(5, 2). Find out which line segments are parallel to each other.a)PQ || RSb)PR || QRc)(1) and (2) bothd)None of theseCorrect answer is option 'A'. Can you explain this answer?
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