Splash Screen Then/Now You graphed points on the coordinate plane. (Lesson 02) Find the distance between two points. Find the midpoint of a segment. Vocabulary distance midpoint segment bisector Concept Or how far is it from one point to the other. Example 1 Find Distance on a Number Line Use the number line to find QR. The coordinates of Q and R are 6 and 3. QR= | 6 (3) |Distance Formula = | 3 | or 3Simplify. Answer: 3 Or how far is it from Q to R? 12 3 A.A B.B C.C D.D Example 1 A.2 B.8 C.2 D.8 Use the number line to find AX. Concept Example 2 Find Distance on a Coordinate Plane Find the distance between E(4, 1) and F(3, 1). (x 1, y 1 ) = (4, 1) and (x 2, y 2 ) = (3, 1) Example 2 Find Distance on a Coordinate Plane CheckGraph the ordered pairs and check by using the Pythagorean Theorem A.4 B. C. D. A.A B.B C.C D.D Example 2 Find the distance between A(3, 4) and M(1, 2). Concept Or find the average of the two endpoints. A.A B.B C.C D.D Example 3 A.330 ft B.660 ft C.990 ft D.1320 ft DRAG RACING The length of a drag racing strip is mile long. How many feet from the finish line is the midpoint of the racing strip? Concept Example 4 Find Midpoint in Coordinate Plane Answer: (3, 3) A.A B.B C.C D.D Example 4 A.(10, 6) B.(5, 3) C.(6, 12) D.(6, 12) Example 5 Find the Coordinates of an Endpoint Write two equations to find the coordinates of D. Let D be (x 1, y 1 ) and F be (x 2, y 2 ) in the Midpoint Formula. Example 5 Find the Coordinates of an Endpoint Answer: The coordinates of D are (7, 11). Midpoint Formula A.A B.B C.C D.D Example 5 A.(3.5, 1) B.(10, 13) C.(15, 1) D.(17, 11) Find the coordinates of R if N (8, 3) is the midpoint of RS and S has coordinates (1, 5). Example 6 Use Algebra to Find Measures Understand You know that Q is the midpoint of PR, and the figure gives algebraic measures for QR and PR. You are asked to find the measure of PR. Example 6 Use Algebra to Find Measures Use this equation and the algebraic measures to find a value for x. Plan Because Q is the midpoint, you know that Solve Subtract 1 from each side. Original measure Example 6 Use Algebra to Find Measures A.A B.B C.C D.D Example 6 A.1 B.3 C.5 D.10