tailieunhanh - Geomegy review 1

Tham khảo tài liệu 'geomegy review 1', ngoại ngữ, anh ngữ phổ thông phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | GEOMETRY REVIEW Midpoint X X1 2 2 32 5 2 1 Midpoint y 71 2 72 5 2 5 2 0 Therefore the midpoint of AB is 1 0 . Slope The slope of a line measures its steepness. Slope is found by calculating the ratio of the change in y-coordinates of any two points on the line over the change of the corresponding x-coordinates slope vertical change horizontal change x2 X1 144 GEOMETRY REVIEW What is the slope of the line shown in the figure on the previous page a. y b. 4 c. 3 d. 2 e. 3 Answer b. To find the slope of a line use the following formula vertical change _ y2 y1 horizontal change X2 x1 slope The two points shown on the line are 1 3 and 5 6 . x1 x2 71 72 1 5 3 6 Plug in the points into the formula _ 6 - 3 slope 5 2 slope 4 Using Slope If you know the slope of a line and one point on the line you can determine other coordinate points on the line. Because slope tells you the ratio of I . you can simply move from the coordinate point you know the horizontal change required number of units determined by the slope. Example A line has a slope of 5 and passes through point 3 4 . What is another point the line passes through The slope is -5 so you know there is a vertical change of 6 and a horizontal change of 5. So starting at point 3 4 add 6 to the y-coordinate and add 5 to the x-coordinate y 4 6 10 x 3 5 8 Therefore another coordinate point is 8 10 . If you know the slope of a line and one point on the line you can also determine a point at a certain coordinate such as the y-intercept x 0 or the x-intercept 0 y . Example A line has a slope of 3 and passes through point 1 4 . What is the y-intercept of the line Slope 44 so you can plug in the coordinates of the known point 1 4 and the unknown point the y-intercept x 0 and set up a ratio with the known slope 4 and solve for x ị x2 x1 3 2 x - 1 3 145 GEOMETRY REVIEW 0 - 4 2 X - 1 3 Find cross products. -4 3 2 x - 1 -12 2x - 2 -12 2 2x - 2 2 _10 _ 2x 2 2 -y x 5 x Therefore the x-coordinate of the y-intercept is 5 .