1.1 and 1.5
Rectangular Coordinates
and Circles
Every man dies, not every man really lives.
-William Wallace
Coordinate Plane
y-axis
Quadrant II
x < 0, y > 0
Quadrant I
x > 0, y > 0
x-axis
Quadrant III
x < 0, y < 0
Quadrant IV
x > 0, y < 0
Distance Formula
Distance Formula
d(P1,P2 )  (x2  x1)2  (y2  y1)2
Midpoint Formula
Midpoint Formula
x1  x 2 y1  y 2 
M  
,

 2
2 
Distance and Midpoint Practice
Practice: Given the points (-9,5) and (4,2)
1) Find the length of the line segment joining the two points
2) Find the midpoint of the line segment joining the two points
Applying Distance Formula
Verify that the triangle with the following vertices is a right
triangle and find its area.
A = (-6,3); B = (3, -5); C = (-1,5)
Equation of a Circle
2
2
2
Standard Form: (x  h)  (y  k)  r
General Form:
x 2  y 2  ax  by  c  0
Circle Practice
1) Write the standard form and general form of the equation
of a circle with center at (4, -3) and radius r = 4
Circle Practice
2) Determine the center (h,k) and radius r of the given circle.
Determine the intercepts and sketch the graph.
2x 2  2y 2  8x 16y  8  0

Circle Practice – Turn In
3) Determine the equation in standard form and general form
for the circle with endpoints of diameter at (4,3) and (0,1).
4) Determine the center (h,k)
and radius r of the given
circle. Determine the
intercepts. Graph in the
calculator to check your
answer.
1.1 and 1.5
Rectangular Coordinates
and Circles
Pg 9 #35, 37, 55, 57, 65
Pg 49 #5, 13, 15, 23*, 29
* Graph on calculator
Every man dies, not every man really lives.
-William Wallace