# Coordinate Geometry

## Transcription

Coordinate Geometry

Intro to Applied and PreCalc Unit: Coordinate Geometry Distance Homework √( ) ( ) Show your work. 1. Find the distance between the following pairs of points to two y decimal places. 10 Example Solution: 8 C Distance between points A and B A 6 Label points A(2, 6) and B(6, -1) ( ) ( ) 4 2 Substitute into formula: ) ( ) √( d -10 -8 -6 2 -2 2 -2 D (6 2) (1 6) 2 -4 -4 (4)2 (7)2 d 16 49 d 65 d -6 -8 -10 d ≈ 8.06 a) B and C b) C and D c) A and D d) B and D e) A and C Page 1 4 6 B 8 10 x Intro to Applied and PreCalc Unit: Coordinate Geometry 2. Bob and Christine want to get together (see map below). Each block is 120 m by 120 m. Assuming the roads are of negligible width, how far does Bob have to travel to reach Christine if: a) he is restricted to the roads? B C b) he can follow a direct path? y 3. Three vertices of a rectangle ABCD are given: A(-3, 1) 5 4 3 B(2, 1)C(-3, 5) 2 1 a) Determine the coordinates of vertex D. -5 -4 -3 -2 -1 1 -1 2 3 4 x 5 -2 b) Find the lengths of the sides. -3 -4 -5 c) Determine the length of the diagonal. 4. A triangle has vertices of A(-2, 5), B(5, 3), and C(0, 2). Find the perimeter of triangle ABC. y 5 4 3 2 1 Classify the triangle as scalene (no equal sides), isosceles (two equal sides), or equilateral (three equal sides). -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 Page 2 1 2 3 4 5 x Intro to Applied and PreCalc Unit: Coordinate Geometry y 5. P is the point (4, 2). Q is a point on the y-axis so that PQ = 5. Find the possible coordinates of Q (two answers). 5 4 3 2 1 -5 -4 -3 -2 -1 1 -1 2 3 4 x 5 -2 -3 -4 -5 y 6. Given the following graph of a line, which of the points (0, 5), (3, 4), (2, 1), (1, 3), (5, -5) and (-1, 7) do not lie on the line? 7 6 5 4 3 2 1 -7 -6 -5 -4 -3 -2 -1-1 -2 -3 -4 -5 -6 -7 Answer Key (Homework) Distance Homework (Page 8-10) 1. a) d = 13.45 units b) d = 11.05 units d) d = 11.18 units e) d = 6.32 units 2. a) 360 metres b) 268.3 metres 3. a) (2, 5) b) 4 units & 5 units 4.dAB = 7.28 dBC = 5.10 dAC = 3.61 5. (0, 5) & (0, -1) 6. (3, 4) does not lie on the line Page 3 1 c) d = 11.40 units c) diagonals = 6.4 units Perimeter = 15.99 units Scalene triangle 2 3 4 5 6 7 x Intro to Applied and PreCalc Unit: Coordinate Geometry Midpoint Homework ( ( ) ( ) ) Show your work 1. Find the midpoint of the following pairs of points. y Example: A and B 10 8 C A (2, 6) and (6, -1) ( ( ) ( ) 4 ) 2 6 6 ( 1) , 2 2 8 5 , 2 2 5 4, or (4, 2.5) 2 a) B and C b) C and D 6 2 -10 -8 -6 D -4 -2 2 -2 4 6 8 10 x B -4 -6 -8 -10 c) A and D 2. The midpoint of AB is the origin. B has coordinates of (3, 7). What are the coordinates of A? Page 4 Intro to Applied and PreCalc Unit: Coordinate Geometry 3. One endpoint of a segment AB is A(-3, 6). If the coordinates of the midpoint are (1, 2), find the coordinates of B. 4. The endpoints of the diameter of a circle are (-6, -2) and (2, 4). Find the circumference and area of the circle correct to three decimal places. C d, A r 2 5. A(1, 1), B(7, 3), C(8, 6) and D(2, 4) are the vertices of parallelogram ABCD. Find the midpoint of AC and the midpoint of BD. Comment on your result. Midpoint Homework 7 2 9 5 , 2 2 1. a) 1, 2. A(-3, -7) 3. (5, -2) 4. Radius = 5 units 5. MAC = MBD = Page 5 b) 3 3 , 2 2 c) C = 31.416 units 9 7 , Midpoints are the same. 2 2 A = 78.540 u2 Intro to Applied and PreCalc Unit: Coordinate Geometry Slope Homework: Textbook Page 132 #1-4, 6, 13 (Answers on Page 276) Table of Values Graphing Homework: Page 6