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If the coordinates of the mid-point of the line segment joining the points (2, 1) and (1, -3) is (x, y), then the relations between x and y can be best described by
  • a)
    3x + 2y = 5
  • b)
    6x + y = 8
  • c)
    5x – 2y = 4
  • d)
    2x – 5y = 4
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If the coordinates of the mid-point of the line segment joining the p...
Midpoint = (2 + 1 / 2, 1 - 3 / 2)
(x, y) = (3/2, -1)
∴ Equation (2) satisfies it.
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Community Answer
If the coordinates of the mid-point of the line segment joining the p...

Explanation:

Given:
Coordinates of point A (2, 1)
Coordinates of point B (1, -3)
Coordinates of the midpoint (x, y)

Formula for finding the midpoint:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

Calculating the midpoint:
x = (2 + 1) / 2 = 3 / 2 = 1.5
y = (1 + (-3)) / 2 = -2 / 2 = -1

Therefore, the midpoint is (1.5, -1)

Equation of the line passing through the two points:
y - y1 = ((y2 - y1) / (x2 - x1))(x - x1)

Substitute the coordinates of point A and B:
y - 1 = ((-3 - 1) / (1 - 2))(x - 2)
y - 1 = -4(x - 2)

Simplify the equation:
y - 1 = -4x + 8
y = -4x + 9

Comparing with the given options:
6x - y = 8

Therefore, the relation between x and y can be best described by option B which is 6x - y = 8.
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If the coordinates of the mid-point of the line segment joining the points (2, 1) and (1, -3) is (x, y), then the relations between x and y can be best described bya)3x + 2y = 5b)6x + y = 8c)5x – 2y = 4d)2x – 5y = 4Correct answer is option 'B'. Can you explain this answer?
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