Homework Sourse1 Find the distance between points 64 and 21 and explain gra
1. Find the distance between points (-6,4) and (2.-1) and explain graphi- cally 2. Find the distance bet ween points (3,0) and (-2, -3) and explain graphi cally 3. Find the distance bet ween points (-5,4) and (6,-1) and explain graphi- cally 4. Write the equation of a circle centered at (-1,-3) with radius 
Solution
Given the two points (x1, y1) and (x2, y2), the distance d between these points is given by the formula:
d = (x2 x1)2 + (y2 y1)2
1) x1 = -6, y1 = 4
x2 = 2, y2 = -1
d = (x2 x1)2 + (y2 y1)2 = (2+ 6)2 + (-1 - 4)2 = (64 + 25) = 89 = 9.43
2) x1 = 3, y1 = 0
x2 = -2, y2 = -3
d = (x2 x1)2 + (y2 y1)2 = (-2 - 3)2 + (-3 - 0)2 = (25 + 9) = 34 = 5.83
3) x1 = -5, y1 = 4
x2 = 6, y2 = -1
d = (x2 x1)2 + (y2 y1)2 = (6 + 5)2 + (-1 - 4)2 = (121 + 25) = 146 = 12.1
4) Center = (-1, -3)
Radius = 5
The standard form of a circle with a center at (h,k) and a radius r is
(xh)2 + (yk)2 = r2
Here h = -1, k = -3, r = 5
Then equation of circle becomes,
(x + 1)2 + (y + 3)2 = 5
