Final answer:
To find the length of DP in triangle ABC, find the equation of the perpendicular bisector, then use the distance formula to calculate the length.
Step-by-step explanation:
To find DP, we need to use the fact that P is the circumcenter of triangle ABC. The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of the triangle intersect.
First, let's find the equation of the line DB. Since D is the midpoint of line AC, we can use the midpoint formula to find its coordinates.
Next, we find the slope of line DB and use it to find the equation of the perpendicular bisector of line DB. This equation will give us the coordinates of the circumcenter P.
Finally, we can find the distance DP by using the distance formula.