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Content Standards G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Mathematical Practices 2 Reason abstractly and quantitatively. 7 Look for and make use of structure. You graphed points on the coordinate plane. • Find the distance between two points. • Find the midpoint of a segment. • distance • irrational number • midpoint • segment bisector 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) | = | –3 | or 3 Answer: 3 Distance Formula Simplify. Use the number line to find AX. Switching both coordinates in the formula will give the same result for the distance. See below. d ( x1 x 2 ) ( y 1 y 2 ) 2 2 Find Distance on a Coordinate Plane Find the distance between E(–4, 1) and F(3, –1). (x1, y1) = (–4, 1) and (x2, y2) = (3, –1) Find Distance on a Coordinate Plane Check Graph the ordered pairs and check by using the Pythagorean Theorem. Draw a sketch of this graph on your paper. Find Distance on a Coordinate Plane . Find the distance between A(–3, 4) and M(1, 2) using the distance formula. Chapter 1 Overview Video Distance and Midpoint Skills Packet Do 7 and 8 (find the distance only) Now let’s do the Reach test questions 1-3 Find Midpoint in Coordinate Plane Answer: M(–3, 3) Class Assignment - 8 minutes Distance and Midpoint Skills Packet Do 4, 5 and 8 (Find the midpoint only) Find the Coordinates of an Endpoint Let D be (x1, y1) and F be (x2, y2) in the Midpoint Formula. (x2, y2) = (–5, –3) Write two equations to find the coordinates of D. Find the Coordinates of an Endpoint Midpoint Formula Midpoint Formula Answer: The coordinates of D are (–7, 11). 5 minutes Skills Packet Do 9 and 10 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. Use Algebra to Find Measures Plan Because Q is the midpoint, you know that Use this equation and the algebraic measures to find a value for x. Solve Subtract 1 from each side. Use Algebra to Find Measures Original measure • Constructions p. 30 ‘Bisect a Segment • HW Skills Packet 1-7, 12-16 all