The correct answer is b) O(0,0), R(3,0), S(3,2), T(0,2), OT=3.
To find the coordinates of the vertices, we look at the given points for each vertex:
- O(0,0): This point is at the origin, so its coordinates are (0,0).
- R(3,0): This point is on the x-axis, so its y-coordinate is 0. The x-coordinate is 3.
- S(3,3): This point is on the line x=3, so its x-coordinate is 3. The y-coordinate is 3.
- T(0,3): This point is on the y-axis, so its x-coordinate is 0. The y-coordinate is 3.
Now let's find the length OT. To find the distance between two points, we can use the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, the coordinates of point O are (0,0) and the coordinates of point T are (0,3).
So, using the distance formula:
OT = sqrt((0 - 0)^2 + (3 - 0)^2)
= sqrt(0 + 9)
= sqrt(9)
= 3
Therefore, the length OT is 3, not 4. So, option d) O(0,0), R(3,0), S(3,3), T(0,3), OT=4 is incorrect.