Two towns are located at   A (2, 2) and   B (8, 10). a. What are the coordinates of the midpoint of   AB.   b. What is the slope of the line that is perpendicular to AB.   c. Find the equation of the perpendicular bisector of   AB. Write your equation in the form   y = mx + c

Two towns are located at   A (2, 2) and   B (8, 10).

a. What are the coordinates of the midpoint of   AB.

b. What is the slope of the line that is perpendicular to AB.

c. Find the equation of the perpendicular bisector of   AB. Write your equation in the form   y = mx + c.

d. Graph A and B on a grid and connect them with a segment. Then accurately graph the perpendicular bisector of AB on the SAME GRAPH.

e. There is another town located at   C (2, 10). Plot point C on the SAME GRAPH and then draw in AC and BC.

      i. Find the midpoint of AC.

     ii. What is the slope of the line perpendicular to AC?

     iii. What is the equation of the perpendicular bisector of AC?

     iv. Graph the perpendicular bisector of AC ONTO THE SAME GRAPH AS BEFORE.

f. Notice that the two perpecdicular bisectors you graphed in part D and part iv are intersecting. Find the point of intersection. Verify your solution by plotting it on your graph. Label the point of intersection as P.

g. Find the following distances using the distance formula. SHOW YOUR WORK. ROUND TO 3 SIGNIFICANT FIGURES.

    i. Find the distance from P to A

   ii. Find the distance from P to B.

   iii. Find the distance from P to C.

h. Explain the significance of point P in relation to point A, point B, and point C.