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The gre quatitative section 3

Tham khảo tài liệu 'the gre quatitative section 3', ngoại ngữ, anh ngữ phổ thông phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | THE GRE QUANTITATIVE SECTION II I - 2 3 2 3 -3 -2 3 -2 III IV Notice that the graph is broken into four quadrants with one point plotted in each one. Here is a chart to indicate which quadrants contain which ordered pairs based on their signs Sign of Points Coordinates Quadrant 2 3 I -2 3 - II -3 -2 - - III 3 -2 - IV Lengths of Horizontal and Vertical Segments Two points with the same y-coordinate lie on the same horizontal line and two points with the same x-coordinate lie on the same vertical line. Find the distance between a horizontal or vertical segment by taking the absolute value of the difference of the two points. Example Find the length of the line segment AB and the line segment BC. 200 THE GRE QUANTITATIVE SECTION Solution 2 - 7 5 AB 1 - 5 4 BC Distance of Coordinate Points To fine the distance between two points use this variation of the Pythagorean theorem d V X2- X1 2 2- yi 2 Example Find the distance between points 2 3 and 1 -2 . Solution d V 1 - 2 2 -2- 3 2 d V 1 -2 2 -2 -3 2 d V -1 2 -5 2 d V1 25 d V26 201 THE GRE QUANTITATIVE SECTION Midpoint To find the midpoint of a segment use the following formula Midpoint X X1 x2 Midpoint y yi l 2 Example Find the midpoint of the segment AB. Solution 1 56 2 1012 Midpoint X 2 2 3 Midpoint y 2 2 6 Therefore the midpoint of AB is 3 6 . Slope The slope of a line measures its steepness. It is found by writing the change in -coordinates of any two points on the line over the change of the corresponding x-coordinates. This is also known as the rise over the run. The last step is to simplify the fraction that results. Example Find the slope of a line containing the points 3 2 and 8 9 . .