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Lesson 1 The Basics of Geometry Review Basic Algebra • • • • • • x + 4 = 16 2x – 11 = 3 (x – 1) . 10 (2 + 5) . 3 = (12 + 1 – 9) ÷2 = 2x – 1 = 5 3 Point You can think of a point as a location. A point has no size. It is represented by a small dot and is named by a capital letter (example, • A). Each point has a location described by two numbers on Cartesian Plane. What is Cartesian Plane? Cartesian Coordinate Plane A Cartesian Coordinate Plane consists of two number lines that intersect. The horizontal number line is called the x – axis and the vertical number line is called the y – axis. The point of intersection of the x – axis and y – axis is called the ORIGIN The axes divide the coordinate plane into four quadrants. Y axis Quadrant II Quadrant I Origin X axis Quadrant III Quadrant IV Any point on the plane can be named by its x and y coordinates. These coordinates are written as an Ordered Pair (x, y). The x and/or y coordinate can be positive and/or negative depending on which quadrant the point is in. To determine the ordered pair of a point you: Read along the xaxis to identify the x value. This is called the x coordinate. Read along the yaxis to identify the y value. This is called the y coordinate. (0, 0) Ex. 1 Plot each point in the Cartesian coordinate plane below. A (4, -5) B(1, 3) C(-2, 4) C B A Ex. 2 Write the coordinates of the points below and identify which quadrant each point is B (5, 5) Quadrant I located. C (-5, 5) Quadrant II D (-6, 2) Quadrant II E (-6, -5) Quadrant III F (0, -6) No Quadrant G (6, -3) Quadrant IV H (4, 0) No Quadrant J (-4, -2) Quadrant III K (1, -4) Quadrant IV L (2, 2) Quadrant I M (-2, 7) Quadrant II N (-2, 3) Quadrant II Shifting Vertically and Horizontally Point Z(3,5) Move 5 units to the left Z Move 7 units down Label the new point as W III W is in quadrant ____ W