in exercises 27-30 find the midpoint of PQ. then write an equation of the line that passes through the midpoint and is perpendicular to PQ. this is called the perpendicular bisector.

Question

28.) P(-5,-5), Q(3,3)

30.) P(-7,0), Q(1,8)

Answer 1

28) midpoint of PQ is ((3-5)/2,(3-5)/2) = (-1,-1)

slope of PQ is (3--5)/(3--5) = 1

slope of perpendicular bisector is negative reciprocal = -1

equation y = mx + b, where m is slope and b is y-intercept

here m = -1 and (-1,-1) is point on line, so

-1 = -(-1) + b

-2 = b

y = -x - 2

30) midpoint of PQ is ((-7+1)/2,(0+8)/2) = (-3,4)

slope of PQ is (8-0)/(1--7) = 1

slope of perpendicular bisector is negative reciprocal = -1

equation y = mx + b, where m is slope and b is y-intercept

here m = -1 and (-3,4) is point on line, so

4 = -(-3) + b

1 = b

y = -x + 1