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