If you know the coordinates of a of points you can: Determine the distance between them. Find the midpoint, slope and equation of a line segment. Determine if lines are parallel or perpendicular. Find the area and perimeter of a polygon defined by the points. Transform a shape by moving, rotating and reflecting it. Define the equations of curves, circles and ellipses. Distance Between Two Points (given their coordinates) Given the of two points, the distance D between the points is given by: where dx is the difference between the x-coordinates of the points and dy is the difference between the of the points. The formula can be used to find the distance between two points when you know the . This distance is also the length of the linking the two points. The distance formula is simply a use of . Notice, is the of a right triangle, where one side is (the difference in and the other is (the dx x-coordinates) dy difference in y-coordinates). From Pythagoras' Theorem we know that: AB2 = dx2 + dy2 Solving this for AB us the formula: Vertical and Horizontal Lines If the line segment is vertical or horizontal, the formula above will still work, but there is an easier way. For a horizontal line, its length is the difference between the x-coordinates. For a vertical line its length is the difference between the y-coordinates. A Practical Application Interactive programs make extensive use of . The computer screens you look at are grids of thousands of tiny dots called pixels that together make up images. Each pixel is addressed using its (x, coordinates. Each pixel y) has a unique pair of coordinates. Programmers use coordinate geometry to code images on the computer screen. Midpoint of a Line Segment Also as the Midpoint Theorem: The of the of a are the average of the coordinates of its endpoints. The midpoint can be found by using the following formula: A line segment on the is defined by two endpoints whose are known. The of this line is exactly halfway between these endpoints and its location can be found using the Midpoint Theorem, which states: The x-coordinate of the midpoint is the average of the x-coordinates of the two endpoints. Likewise, the y-coordinate is the average of the y-coordinates of the endpoints. Along the x-axis: midway between 10 and 50 is 30. Along the y-axis: midway between 10 and 20 is 15.
If you know the coordinates of a of points you can: Determine the distance between them. Find the midpoint, slope and equation of a line segment. Determine if lines are parallel or perpendicular. Find the area and perimeter of a polygon defined by the points. Transform a shape by moving, rotating and reflecting it. Define the equations of curves, circles and ellipses. Distance Between Two Points (given their coordinates) Given the of two points, the distance D between the points is given by: where dx is the difference between the x-coordinates of the points and dy is the difference between the of the points. The formula can be used to find the distance between two points when you know the . This distance is also the length of the linking the two points. The distance formula is simply a use of . Notice, is the of a right triangle, where one side is dx (the difference in x-coordinates) and the other is dy (the difference in y-coordinates). From Pythagoras' Theorem we know that: AB2 = dx2 + dy2 Solving this for AB us the formula: Vertical and Horizontal Lines If the line segment is vertical or horizontal, the formula above will still work, but there is an easier way. For a horizontal line, its length is the difference between the x-coordinates. For a vertical line its length is the difference between the y-coordinates. A Practical Application Interactive programs make extensive use of . The computer screens you look at are grids of thousands of tiny dots called pixels that together make up images. Each pixel is addressed using its (x, y) coordinates. Each pixel has a unique pair of coordinates. Programmers use coordinate geometry to code images on the computer screen. Midpoint of a Line Segment Also as the Midpoint Theorem: The of the of a are the average of the coordinates of its endpoints. The midpoint can be found by using the following formula: A line segment on the is defined by two endpoints whose are known. The of this line is exactly halfway between these endpoints and its location can be found using the Midpoint Theorem, which states: The x-coordinate of the midpoint is the average of the x-coordinates of the two endpoints. Likewise, the y-coordinate is the average of the y-coordinates of the endpoints. Along the x-axis: midway between 10 and 50 is 30. Along the y-axis: midway between 10 and 20 is 15.
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