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

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?

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.