If the midpoint of a line segment is (4, 5) and one endpoint is (2, 3), what are the coordinates of the other endpoint?

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Q: If the midpoint of a line segment is (4, 5) and one endpoint is (2, 3), what are the coordinates of the other endpoint?

Solution: Let the other endpoint be (x, y). The midpoint formula gives (2 + x)/2 = 4 and (3 + y)/2 = 5. Solving these gives x = 6 and y = 7.

Steps: 9

Step 1: Identify the given information. The midpoint is (4, 5) and one endpoint is (2, 3).
Step 2: Let the other endpoint be (x, y).
Step 3: Use the midpoint formula for the x-coordinates: (2 + x) / 2 = 4.
Step 4: Multiply both sides of the equation by 2 to eliminate the fraction: 2 + x = 8.
Step 5: Subtract 2 from both sides to solve for x: x = 6.
Step 6: Use the midpoint formula for the y-coordinates: (3 + y) / 2 = 5.
Step 7: Multiply both sides of the equation by 2: 3 + y = 10.
Step 8: Subtract 3 from both sides to solve for y: y = 7.
Step 9: Combine the values of x and y to find the other endpoint: (6, 7).