Final answer:
The median AP of triangle AART, connecting vertex A to the midpoint P of side RT, has a length of 5 units.
Step-by-step explanation:
To determine the length of the median AP of triangle AART, we must first find the midpoint P of side RT. The coordinates of the midpoint are calculated by averaging the x-coordinates and the y-coordinates of points R and T separately. This gives us the midpoint P as ((3+7)/2, (4+2)/2) which simplifies to P(5, 3). Now, we use the distance formula to calculate the length of AP, which connects vertex A to midpoint P:
AP = √[(5-1)² + (3-0)²] = √[16 + 9] = √25 = 5 units.
The length of the median AP is therefore 5 units.