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Rectangular Coordinate System: The Cartesian Plane 1.1, and Review Review: Equations 9x − 10 = 5x + 2(2x − 5) 17+y y √ + 32+y y = 100 5−x−3=2 |2x + 1| = 7 Vocab. ! coordinate pair – (x, y) ! x-coordinate ! y-coordinate ! x-axis and y-axis ! the origin ! quadrants Formulas ! Midpoint Formula ! Given 2 points (x1, x2) and (y1, y2) the midpoint, M, is: 2 y1 +y2 M ( x1 +x , 2 ) 2 ! Distance Formula ! Given 2 points (x1, x2) and (y1, y2) the distance between them, d, is: d= � (x2 − x1 )2 + (y2 − y1 )2 ! Pythagorean Theorem (only works for right triangles) where h is the length of the hypotenuse and a & b are the length of the legs a 2 + b 2 = h2 Examples: ! Ex. 1: Find coordinates of a point 10 units to the left of y-axis and 3 units above the x-axis. ! Ex. 2: If –x > 0 and y < 0, what quadrant is (x, y) in? Examples cont. ! Ex. 3: : Find the distance between (-3, -2) and (4, 1). ! Ex. 4: Find the midpoint of the line segment between (5, 2) and (-3, -1). Examples cont. ! Ex. 5: An airplane flies from Naples, Italy in a straight line to Rome, Italy, which is 120 km north and 150 km west of Naples. How far does the plane fly? Examples cont. ! Ex. 6: A room is 1½ times as long as it is wide, and its perimeter is 25 meters. Find the dimensions of the room. Review: Inequalities 1 < 2x + 3 ≤ 9 −4(x + 1) < 2x + 3 |x − 20| ≤ 6 |9 − 2x| − 2 > −1 Identify & Correct the error: Ex. 1: 5 ÷ 50 = 50 ÷ 5 Ex. 2: 8 − (x + 2) = (8 + 2) + x = x +10 Identify & Correct the error: Ex. 3: 2 2 (a + b) = a + b 2 Ex. 4: € 1 (1/ x) + 2 = x +2 Identify & Correct the error: Ex. 5: 3 2x = (2x) 3 Ex. 6: € −x + k = − x − k Identify & Correct the error: Ex. 7: m m m = + x+n x n Ex. 8: € a + bx = 1+ bx a