1. GEOMETRY HELP d = 8 2 + (–8) 2 Simplify. Find the distance between R(–2, –6) and S(6, –2) to the nearest tenth. Let (x 1, y 1 ) be the point R(–2, –6) and (x 2, y 2 ) be the point S(6, –2). To the nearest tenth, RS = 11.3. d = (x 2 – x 1 ) 2 + (y 2 – y 1 ) 2 Use the Distance Formula. d = (6 – (–2)) 2 + (–2 – (–6)) 2 Substitute. d = 64 + 64 = 128 Quick Check The Coordinate Plane LESSON 1-8 Additional Examples 128 Use a calculator.

2. GEOMETRY HELP Jackson has coordinates (2, 4). Let (x 1, y 1 ) represent Jackson. Elm has coordinates (–3, –6). Let (x 2, y 2 ) represent Elm. To the nearest tenth, the subway ride from Jackson to Elm is 11.2 miles. d = (–5) 2 + (–10) 2 Simplify. d = (x 2 – x 1 ) 2 + (y 2 – y 1 ) 2 Use the Distance Formula. How far is the subway ride from Jackson to Elm? Round to the nearest tenth. d = (–3 – (2)) 2 + (–6 – (4)) 2 Substitute. d = 25 +100 = 125 The Coordinate Plane LESSON 1-8 Additional Examples Quick Check 125 Use a calculator.

3. GEOMETRY HELP Use the Midpoint Formula. Let (x 1, y 1 ) be A(8, 9) and (x 2, y 2 ) be B(–6, –3). The coordinates of midpoint M are (1, 3). AB has endpoints (8, 9) and (–6, –3). Find the coordinates of its midpoint M. The midpoint has coordinatesMidpoint Formula (, ) x 1 + x 2 2 y 1 + y 2 2 Substitute 8 for x 1 and (–6) for x 2. Simplify. 8 + (–6) 2 The x–coordinate is = = 1 2222 Substitute 9 for y 1 and (–3) for y 2. Simplify. 9 + (–3) 2 The y–coordinate is = = 3 6262 The Coordinate Plane LESSON 1-8 Additional Examples Quick Check

4. GEOMETRY HELP Find the x–coordinate of G.Find the y–coordinate of G. 4 + y 2 2 5 = 1 + x 2 2 –1 = Use the Midpoint Formula. The coordinates of G are (–3, 6). The midpoint of DG is M(–1, 5). One endpoint is D(1, 4). Find the coordinates of the other endpoint G. –2 = 1 + x 2 10 = 4 + y 2 Multiply each side by 2. Use the Midpoint Formula. Let (x 1, y 1 ) be D(1, 4) and the midpoint be (–1, 5). Solve for x 2 and y 2, the coordinates of G. (,)(,) x 1 + x 2 2 y 1 + y 2 2 –3 = x 2 6 = y 2 The Coordinate Plane LESSON 1-8 Additional Examples Quick Check