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Difficulty: 1/102022 NMTC 2022 (QII-59)

Midpoint of and is ________.

Guide / Hint

Hint 1: Use the midpoint coordinates formula: and .

Hint 2: Substitute the given coordinates and into the formula.

Hint 3: Simplify the fractions to obtain the coordinates of the origin, which represents the midpoint of these symmetric points.

Solution

Step 1 (Midpoint Formula): The coordinates of the midpoint of two points and are given by:

Step 2 (Substitute coordinates): We substitute and :

Step 3 (Conclusion): The midpoint is exactly (0,0) (the origin).

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    2022 NMTC 2022 QII-59 - Olympiad Math Olympiad Question | Leminno