P.2 Cartesian Coordinate System

Cartesian Plane: Points in a plane correspond to ordered pairs of real #s The Coordinate Plane is divided into 4 quadrants.

Absolute value The absolute value of a real number is it’s distance from zero Example: |-8| = 8 |11|= 11 What is the Absolute value of: a) |-4|= ? b) |π – 6| = ? a) 3 b) ≈ 2.858

Distance Formula (Number Line) The distance between a and b |a-b| Between two points the distance formula is |x1 – x2| = |x2 – x1| |y1 – y2| = |y2 – y1| Distance Formula (coordinate plane) The distance formula in the coordinate plane is d = √ (x1 – x2)2 + (y2 – y1)2 Midpoint Formula Whe the endpoints of a segment in a number line are known, we take the average of their coordinates to find the midpoint of the segment. The midpoint of the line segment with endpoints a and b is: a+b 2

The standard form equation of a circle with center (h,k) and radius r is (x – h)2 + (y – k)2 = r2 Ex: center (-4,1), radius 8 (x – (-4))2 + (y – (1))2 = 82 Using an inquality to express distance We can state the distance between x and -3 is less that 9 using the inequality |x- (-3)| < 9 Or |x + 3| < 9

Practice: 1.Find x and y: Center (1,2), r = 5 Center (0,0), r = √3 Find the center and radius: (x – 3)2 + (y – 1)2 =36 2. Write a statement: Distance blt x and 4 is 3 Distance blt y and -2 is ≥4 (5,5) is the midpoint, (1,2) = a,c find b,d

Find the distance between the points 11. -9. 2, 10. 6 13 Find the distance between the points 11. -9.2, 10.6 13. (-3,-1), (5,-1) Find the area and perimeter of the figure: 19. (-5,3), (0,-1), (4,4) Find the midpoint: 24. -5,-17 28. (5,-2), (-1,-4)

Good Luck