Midpoint and Distance in the Coordinate Plane

Midpoint and Distance in the Coordinate Plane Geometry (Holt 1-6) K.Santos

Coordinate Plane Coordinate plane—is a plane that is divided into four regions (quadrants) by a horizontal line (x-axis) and a vertical line (y-axis). The location, or coordinates of a point are given by an ordered pair (x, y). y x

Midpoint Formula The midpoint M of with endpoints A(, ) and B(, ) are the following: M = (, ) A(, ) midpoint B(, ) Find the average of the coordinate values

Example--FINDING THE MIDPOINT Find the coordinates of the midpoint (M) of with endpoints (8, 9) and (-6, 3). Think: (8, 9) and (-6, 3) , Use the midpoint formula: M = (, ) (, ) (, The midpoint M is located at (1, 6)

Example--Finding the endpoint M is the midpoint of . D has coordinates (1, 4) and M has coordiantes (-1, 5). Find the coordinates of G. Remember the midpoint formula: M = (, ) G(x, y) -1 = 5= -2 = 1 + x 10= 4 +yM(-1, 5) -3 = x 6 = y D(1, 4) So the other endpoint is at G(-3, 6)

Distance formula In the coordinate plane, the distance between two points (, ) and (, is: d = B(, A(, )

Example---Distance Find the distance between: A(7, 9) and B(-5, -3) ,, A d = B 12 This is also the length of the segment (AB = 12

Example—Congruent Segments Find FG and JK. Then determine whether ≅ . F(1, 2), G(5, 5), J(-4, 0) and K(-1, -3) FG = JK = JK = FG = JK = FG= =JK = FG = JK= FG = 5 JK = 3 The segments are not congruent.

Midpoint and Distance in the Coordinate Plane