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- 49 - GMAT Club Math Bookpart of GMAT ToolKit iPhone AppShould both of the lines be tangents to the circle, point A coincides with point D, point C coincides with point B, and the theorem still applies: Practice from the GMAT Official Guide: The Official Guide, 12th Edition: DT #36; PS #33; PS #160; PS #197; PS #212; DS #42; DS #96; DS #114; DS #117; DS #160; DS #173; The Official Guide, Quantitative 2th Edition: PS #33; PS #141; PS #145; PS #153; PS #162; DS #22; DS #58; DS #59; DS #95; DS #99; The Official Guide, 11th Edition: DT #36; PS #30; PS #42; PS #100; PS #160; PS #206; PS #229; DS #23; DS #76; DS #86; DS #136; DS #152.
- 50 - GMAT Club Math Bookpart of GMAT ToolKit iPhone AppCoordinate GeometryDefinitionCoordinate geometry, or Cartesian geometry, is the study of geometry using a coordinate system and the principles of algebra and analysis. The Coordinate PlaneIn coordinate geometry, points are placed on the "coordinate plane" as shown below. The coordinate plane is a two-dimensional surface on which we can plot points, lines and curves. It has two scales, called the x-axis and y-axis, at right angles to each other. The plural of axis is 'axes' (pronounced "AXE-ease"). A point's location on the plane is given by two numbers, one that tells where it is on the x-axis and another which tells where it is on the y-axis. Together, they define a single, unique position on the plane. So in the diagram above, the point A has an x value of 20 and a y value of 15. These are the coordinates of the point A, sometimes referred to as its "rectangular coordinates". X axisThe horizontal scale is called the x-axis and is usually drawn with the zero point in the middle. Values to the right are positive and those to the left are negative. Y axisThe vertical scale is called the y-axis and is also usually drawn with the zero point in the middle. Values above the origin are positive and those below are negative. OriginThe point where the two axes cross (at zero on both scales) is called the origin. QuadrantsWhen the origin is in the center of the plane, they divide it into four areas called quadrants.
- 51 - GMAT Club Math Bookpart of GMAT ToolKit iPhone AppThe first quadrant, by convention, is the top right, and then they go around counter-clockwise. In the diagram above they are labeled Quadrant 1, 2 etc. It is conventional to label them with numerals but we talk about them as "first, second, third, and fourth quadrant". Point (x,y)The coordinates are written as an "ordered pair". The letter P is simply the name of the point and is used to distinguish it from others. The two numbers in parentheses are the x and y coordinates of the point. The first number (x) specifies how far along the x (horizontal) axis the point is. The second is the ycoordinate and specifies how far up or down the y axis to go. It is called an ordered pair because the order of the two numbers matters - the first is always the x (horizontal) coordinate.