1 7 Midpoint and Distance in the Coordinate

1 -7: Midpoint and Distance in the Coordinate Plane Part I

Today’s Objective Given two endpoints of a segment, we can solve for the midpoint of that segment. Given two points on a coordinate plane, we can solve for the midpoint. Given the midpoint and one endpoint, we can solve for the other endpoint.

The Midpoint AM = 5 =MB Midpoint on a number line: Average of two endpoints A M B -3 2 7

The Midpoint A On a Coordinate Plane Average of the x-coordinate and the average of the y-coordinate M B

Finding the Midpoint The midpoint is (1, 4) Find the midpoint between A(-4, 6) and B(6, 2) A Solve for the x-coordinate M Solve for the y-coordinate B

The Midpoint Formula Average of the x’s Average of the y’s Notice the Midpoint is an ordered pair (x, y)

Example Find the midpoint between A(-3, 2) and B(-7, 12).

Example Find the midpoint between A(15, 0) and B(-2, -16).

Finding an Endpoint A (-5, 0) M B(5, 1)

Finding an Endpoint Algebraically ENDPOINT IS (2, -2) Endpoint (-4, 6) with Midpoint (-1, 2) Solve for x-coordinate Solve for y-coordinate

Example ENDPOINT IS (1, -5) Given M(-2, 1) is the midpoint of LM and one endpoint is L(-5, 7), what are the coordinates of M? Solve for x-coordinate Solve for y-coordinate

Take Home Message The midpoint is simply the average of the x-coordinates, and the average of the y-coordinates. Whether on a number line or on a coordinate plane, the midpoint cuts a segment into two congruent parts.