The points P ( -5, 6),  Q ( -3, 8) and R(3, 2) are joined to form a triangle. a Show that angle PQR is a right angle.
b Find the equation of the circle that passes through the points P, Q and R

Detail steps below

Step-by-step explanation:

a.  PQ² + QR² = ((-5 - -3)² + (6 - 8)²) + ((-3 - 3)² + (8 - 2)²) = 8 + 72 = 80

    PR² = (-5 - 3)² + (6 - 2)² = 80

PQ² + QR² = PR²    ... PQR is right triangle

b. Circle circumscribe PQR, center of circle is the midpoint of hypotenuse

   O (h,k): h=1/2(-5 + 3) = -1      k=1/2(6+2) = 4     center O (-1 , 4)

   radius = 1/2 PR = 1/2*√80 = 2√5

equation: (x-h)² + (y-k)² = r²      (x+1)² + (y-4)² = 20

 

a=24; b=12

step-by-step explanation:

a/b=2: 1

a=2b

36/(1+2)=12

b=12

a=24

she will travel a distance in the range of 3 - 11 miles