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If the coordinates of point D are (5, 5) and it is the midpoint of line segment

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Question: If the coordinates of point D are (5, 5) and it is the midpoint of line segment joining points E(3, 1) and F(x, y), what are the coordinates of F?

Options:

  1. (7, 9)
  2. (9, 7)
  3. (8, 6)
  4. (6, 8)

Correct Answer: (9, 7)

Solution: 

Using the midpoint formula: D = ((x1 + x2)/2, (y1 + y2)/2). Solving gives F(7, 9).

If the coordinates of point D are (5, 5) and it is the midpoint of line segment

Practice Questions

Q1
If the coordinates of point D are (5, 5) and it is the midpoint of line segment joining points E(3, 1) and F(x, y), what are the coordinates of F?
  1. (7, 9)
  2. (9, 7)
  3. (8, 6)
  4. (6, 8)

Questions & Step-by-Step Solutions

If the coordinates of point D are (5, 5) and it is the midpoint of line segment joining points E(3, 1) and F(x, y), what are the coordinates of F?
  • Step 1: Identify the coordinates of point D, which are (5, 5).
  • Step 2: Identify the coordinates of point E, which are (3, 1).
  • Step 3: Use the midpoint formula: D = ((x1 + x2)/2, (y1 + y2)/2).
  • Step 4: In the formula, let (x1, y1) be the coordinates of point E (3, 1) and (x2, y2) be the coordinates of point F (x, y).
  • Step 5: Substitute the known values into the midpoint formula: (5, 5) = ((3 + x)/2, (1 + y)/2).
  • Step 6: Set up two equations from the midpoint formula: 5 = (3 + x)/2 and 5 = (1 + y)/2.
  • Step 7: Solve the first equation: Multiply both sides by 2 to get 10 = 3 + x, then subtract 3 from both sides to find x = 7.
  • Step 8: Solve the second equation: Multiply both sides by 2 to get 10 = 1 + y, then subtract 1 from both sides to find y = 9.
  • Step 9: Combine the values of x and y to find the coordinates of point F, which are (7, 9).
  • Midpoint Formula – The midpoint formula is used to find the midpoint of a line segment given the coordinates of its endpoints.
  • Coordinate Geometry – Understanding how to manipulate and solve for coordinates in a Cartesian plane.
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