Chapter 1.3 Notes: Use Midpoint and Distance Formulas Goal: You will find lengths of segments in the coordinate plane.

Midpoints and Bisectors: The midpoint of a segment is the point that divides the segment into two congruent segments. A segment bisector is a point, ray, line, line segment, or plane that intersects the segment at its midpoint. A midpoint or a segment bisector bisects a segment.

Ex.1: In the skateboard design, bisects at point T, and XT = 39.9 cm. Find XY.

Ex.2: Point M is the midpoint of. Find the length of.

Ex.3: Identify the segment bisector of. Then find PQ.

To find the midpoint using coordinates in a coordinate plane, you will use the Midpoint Formula. The Midpoint Formula: If A(x 1, y 1 ) and B(x 2, y 2 ) are points in a coordinate plane, then the midpoint M of has coordinates – Midpoint =

Ex.4: The endpoints of RS are R(1, -3) and S(4, 2). Find the coordinates of the midpoint M. Ex.5: The midpoint of JK is M(2, 1). One endpoint is J(1, 4). Find the coordinates of endpoint K. Ex.6: The endpoints of GH are G(7, -2) and H(-5, -6). Find the coordinates of the midpoint P. Ex.7: The midpoint of AB is M(5, 8). One endpoint is A(2, -3). Find the coordinates of endpoint B.

Distance Formula: To find the distance between two points, you will always use the Distance Formula. The Distance Formula: If A(x 1, y 1 ) and B(x 2, y 2 ) are points in a coordinate plane, then the distance between A and B is distance (d) =

Ex.8: What is the approximate length of RS with endpoints R(2, 3) and S(4, -1)? Ex.9: What is the approximate length of AB with endpoints A(-3, 2) and B(1, -4)? Ex.10: What is the difference between these three symbols: =,, and ≈?