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20 3 10 3 20 2 10 2 4. Find the perimeter of a square whose diagonal is 6 2 . (A) 24 (B) 12 2 (C) 12 (D) 20 (E) 24 2 Find the length of DB. 5. 2. Two boats leave the same dock at the same time, one traveling due west at 8 miles per hour and the other due north at 15 miles per hour. How many miles apart are the boats after three hours? (A) 17 (B) 69 (C) 75 (D) 51 (E) 39 (A) (B) (C) (D) (E) 8 10 12 15 20 www.petersons.com 208 Chapter 13 4. COORDINATE GEOMETRY
A. Distance between two points = ( x2 − x1 )2 + ( y2  y1 )2
The distance between (–3, 2) and (5, –1) is −3 − 5 + 2  ( 1) = 2 2 (8)2 + (3)2 = 64 + 9 = 73 B. The midpoint of a line segment = x1 + x 2 y1 + y2 2,2 Since a midpoint is in the middle, its coordinates are found by averaging the x coordinates and averaging the y coordinates. Remember that to find the average of two numbers, you add them and divide by two. Be very careful of signs in adding signed numbers. Review the rules given earlier if necessary. The midpoint of the segment joining (–4, 1) to (–2, –9) is −4 + ( 2 ) 1 + ( 9 ) 6 8 = ( 3,4 ) , , = 2 2 2 2 Exercise 4
Work out each problem. Circle the letter that appears before your answer. 1. AB is the diameter of a circle whose center is O. If the coordinates of A are (2, 6) and the coordinates of B are (6, 2), find the coordinates of O. (A) (4, 4) (B) (4, –4) (C) (2, –2) (D) (0, 0) (E) (2, 2) AB is the diameter of a circle whose center is O. If the coordinates of O are (2, 1) and the coordinates of B are (4, 6), find the coordinates of A. (A) (B) (C) (D) (E)
1 3, 3 2 3. Find the distance from the point whose coordinates are (4, 3) to the point whose coordinates are (8, 6). (A) 5 (B) 25 (C) 7 (D) (E)
67 15 2. 4. 1 1, 2 2 The vertices of a triangle are (2, 1), (2, 5), and (5, 1). The area of the triangle is (A) 12 (B) 10 (C) 8 (D) 6 (E) 5 The area of a circle whose center is at (0,0) is 16π. The circle passes through each of the following points except (A) (4, 4) (B) (0, 4) (C) (4, 0) (D) (–4, 0) (E) (0,...
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