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Find Coordinates of Point A in Square OCAB with Area 9
Published on August 6, 2024
Geometry
Find the coordinates of point A in square OCAB with an area of 9 square units, where point O is at the origin. The solution reveals that point A is located at (3, 3).
Question
Square OCAB has an area of 9 square units. Point O is found where the axes meet. What are the coordinates of point A?
Answer
Here’s how to solve the problem step-by-step:
1. Find the side length of the square.
- The area of a square is side length * side length (s*s or s²)
- We know the area is 9 square units, so s² = 9
- Taking the square root of both sides, we find the side length (s) = 3 units.
2. Determine the coordinates of point A.
- Point O is at the origin (0,0).
- Since OCAB is a square, point A is 3 units to the right of point O along the x-axis and 3 units up from point O along the y-axis.
Therefore, the coordinates of point A are (3, 3).