It is convenient to do part b first, then use that result to do part a.
b. For some pair of points (x1, y1) and (x2, y2), you want to find a point (a, b) such that (a, b) - (x1, y1) = (x2, y2) - (a, b). That is, the differences of coordinates from one end to the center are the same as the differences from the center to the other end. Adding (a, b) to the above equation gives 2(a, b) - (x1, y1) = (x2, y2) Adding (x1, y1) then gives 2(a, b) = (x1, y1) + (x2, y2) Finally, dividing by 2 gives a formula for (a, b):
(a, b) = ((x1, y1) + (x2, y2))/2 The midpoint is the average of the end points.
a. Using the result from part b, the midpoint is midpoint = ((2, 3) + (6, 7))/2 = (8, 10)/2 midpoint = (4, 5)
The angle supplementary to 115° is 180 - 115 = 65° and the angle that forms a full circle with 304° is 360 - 304 = 56°. Since the measure of an exterior angle is equal to the sum of its remote interior angles, we know that x = 65 + 56 = 121°.
