Final answer:
To find the coordinates of B in the right triangle OAB with O at the origin, and |OA| = |AB| where A's coordinates are (3, 2), we identify the triangle as isosceles with the right angle at O. Using Pythagorean theorem and the fact that B lies on the y-axis, we deduce that the coordinates of B are (0, 2).
Step-by-step explanation:
To find the coordinates of point B in the right triangle OAB where O is the origin (0,0), |OA|=|AB|, and the coordinates of A are (3, 2), we can follow these steps:
- First, notice that the triangle is isosceles since |OA| = |AB|, and OA is a segment from the origin to A.
- As OAB is a right triangle with the right angle at O, the coordinates of A (3,2) also represent the lengths of the legs of the triangle from O to A along the x-axis and y-axis, respectively.
- To find the coordinates of B, we will use the fact that triangle OAB is isosceles, so the distance from O to B will be the same as from O to A, and the length of OB will also be √(3² + 2²) = √13.
- Since B lies on a circle centered at the origin with radius √13, and OA forms one leg of the triangle, B will be the other leg sticking out from the y-axis, meaning B has the same y-coordinate as A, which is 2.
- Finally, since B is on the x-axis and OB is the hypotenuse, we find the x-coordinate of B using the Pythagorean theorem: √(13 - 2²) which is √(13 - 4) = √9 = 3.
Therefore, the coordinates of B are (0, 2).