Midpoint and Distance in the Coordinate Plane SEI.3.AC.4: Use, with and without appropriate technology, coordinate geometry to represent and solve problems including midpoint, length of a line segment and Pythagorean Theorem.

FHSChapter 12 The Coordinate Plane Review The coordinate plane is a plane divided into 4 regions by the x -axis and the y -axis. These 4 areas are called quadrants. Here are the four quadrants: x y 0 I IVIII II The 0 in the center is called the origin.

FHSChapter 13 Graphing Points Review The first number tells us to go right or left and the second number tells us to go up or down. Let’s look at some examples: (2, 3) (-1, -2) x y 0 (-3, 2) (2, -2) The location, or coordinates, of a point are given by an ordered pair ( x, y )

FHSChapter 14 Midpoint Formula You can find the midpoint of a segment by using the coordinates of its endpoints. The midpoint of the segment joining the points A(x 1, y 1 ) and B(x 2, y 2 ) has these coordinates: Example: Find the midpoint of A (-1, 4) & B (3, 5).

FHSChapter 15 Distance Formula In the coordinate plane, the formula for the distance between the points A(x 1, y 1 ) and B(x 2, y 2 ) is: Example: Find AB; A(-1,3) and B(3,-2) A B

FHSChapter 16 Lesson Quiz 1.Find the coordinates of the midpoint of MN with endpoints M(-2, 6) and N (8, 0). 2.K is the midpoint of HL. H has coordinates (1, –7), and K has coordinates (9, 3). Find the coordinates of the other endpoint. 3.Find the distance, to the nearest tenth, between S(6, 5) and T(–3, –4). (17, 13) (3, 3) 12.7