8.1 The Rectangular Coordinate System and Circles Part 1: Distance and Midpoint Formulas

Rectangular Coordinates A pair of numbers in the form (x, y) is an example of an ordered pair. The numbers in an ordered pair are the components of the ordered pair. An ordered pair is plotted (or graphed) on a rectangular (or Cartesian) coordinate system. The axes from four quadrants. (A point on an axis is not considered to be in any quadrant.) x-axis y-axis I II III IV origin

Distance Formula The distance between the points (x 1, y 1 ) and (x 2, y 2 ) is

Finding the Distance Between Two Points Find the distance between (-3, 5) and (6, 4).

 Find the distance between (3, 4) and (-2, 1).

Midpoint Formula The midpoint of a line segment is the point on the segment that is equidistant from both endpoints. Given the coordinates of the two endpoints of a line segment, we can find the midpoint by “averaging” the coordinates…or by using

Finding the Midpoint of a Segment Find the coordinates of the midpoint of the line segment with endpoints (8, -4) and (-9, 6).

 Find the coordinates of the midpoint of the line segment with endpoints (3, 4) and (-2, 1).

Graphing in the Third Dimension (NOT in the book!) A 3-dimensional graph has a z-axis along with the x- and y-axis, so points have 3 coordinates: (x, y, z). 3-D Distance Formula 3-D Midpoint Formula