Geometry Notes Name_________________________ Warm Up 1. What would be another way to write FG ? 2. Point S is between R and T on RT. Solve the equation. Then find RS and ST. RS = 2x – 8 ST = 3x – 10 RT = 17 3. Find DE. 63 D E F 51 Today, we will Define midpoint and bisector Learn and apply the midpoint and distance formula Midpoint and Distance Formulas Lengths are equal Segments are congruent AB = CDA B C D “is equal to” AB CD “is congruent to” A _____________________ divides a segment into two congruent segments. A ____________________________________ is anything that intersects the segment at the midpoint. C M A M M is the midpoint B A B D CD is a segment bisector of AB Example 1 In the diagram RT bisects UV at point S. US = 42.5 cm. Find UV. V T S R U Example 2 If M is the midpoint of CD find the length of CM. 7x - 2 6x + 4 C M D Midpoint Formula x1 x 2 y1 y 2 , 2 2 Example 3 a. The endpoints of GH are G(2, –4) and H(3, 3). Find the coordinates of the midpoint M. b. The endpoints of AB are A(3, 5) and B(7, –9). Find the coordinates of the midpoint M. c. The midpoint of XY is M(1, 2). One endpoint is X(4, 1). Find the coordinates of endpoint Y. d. The midpoint of JK is M(6, 3). One endpoint is J(4, –2). Find the coordinates of endpoint K. Distance Formula AB (x 2 x 1 ) 2 (y 2 y 1 ) 2 Example 4 Use the distance formula to find the distance between the two given points. a. (2, –6), (5, –2) b. (4, 9), (12, 3) c. (2, 3), (4, –1) d. (–3, 2), (1, –4) **The following information will not be on your video notes. We will do this together in class next time!** Constructing Segment Bisectors A ___________________________ is a geometric drawing that uses a limited set of tools, usually a compass and a straightedge. How to… 1. copy a segment A C 2. bisect a segment B A B