1.1 and 1.5 rectangular coordinates and circles every man dies, not every man really lives. -william...

1.1 and 1.5Rectangular Coordinates

and Circles

Every man dies, not every man really lives.-William Wallace

Coordinate Plane

Quadrant Ix > 0, y > 0

Quadrant IIx < 0, y > 0

Quadrant IVx > 0, y < 0

Quadrant IIIx < 0, y < 0

x-axis

y-axis

Distance Formula

d(P1,P2) (x2 x1)2 (y2 y1)

2

Distance Formula

Midpoint Formula

M x1 x2

2, y1 y2

2

Midpoint Formula

Distance and Midpoint PracticePractice: 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 FormulaVerify 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

Standard Form:

(x h)2 (y k)2 r2

General Form:

x 2 y 2 ax by c 0

Circle Practice1) Write the standard form and general form of the equation of a circle with center at (4, -3) and radius r = 4

Circle Practice2) 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 In3) 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 1.5Rectangular Coordinates

and Circles

Every man dies, not every man really lives.-William Wallace

Pg 9 #35, 37, 55, 57, 65Pg 49 #5, 13, 15, 23*, 29*

* Graph on calculator