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CHAPTER 12 Analytic Geometry
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(12.17) 3x 7 2x 8 2 4x
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12.44. State the equation of a line which has a y- intercept of (a) 5 and a slope of 4 (b) 2 and a slope of (c) 3 (d) 8 and is parallel to y (e) 3 and is parallel to y
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1 1 and a slope of 3
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(f) 0 and is parallel to y
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12.45. State the equation of a line which has a slope of 2 and passes through (a) (1, 4); (b) ( 2, 3); (c) ( 4, 0); (d) (0, 7). (12.17) 12.46. State the equation of a line (a) Which passes through the origin and has a slope of 4
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1 (b) Which passes through (0, 3) and has a slope of 2
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(12.17)
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(c) Which passes through (1, 2) and has a slope of 3 (d) Which passes through ( 1, 2) and has a slope of 1 3
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(e) Which passes through the origin and is parallel to a line that has a slope of 2 12.47. (a) Describe the locus of the equation x2 y2 49. (12.18)
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(b) State the equation of the locus of points 4 units from the origin. (c) State the equations of the locus of points 3 units from the locus of x2 y2 25. y2 16; (c) the circle (12.18)
12.48. State the equation of the locus of point 5 units from (a) the origin; (b) the circle x2 x2 y2 49. 12.49. What is the radius of the circle whose equation is (a) x2 (d) x
9; (b) x2
16 9;
(c) 9x2
(12.18)
12.50. What is the equation of a circle whose center is the origin and whose radius is (a) 4; (b) 11; (c) 2; (d) 11; (e) 25; 3 2 (f) 1 23 (12.18) 3 12.51. Find the area of ^ABC, whose vertices are A(0, 0) and (a) B(0, 5) and C(4, 5) (b) B(0, 5) and C(4, 2) 12.52. Find the area of a (a) Triangle whose vertices are A(0, 0), B(3, 4), and C(8, 0) (b) Triangle whose vertices are D(1, 1), E(5, 6), and F(1, 7) (c) Rectangle three of whose vertices are H(2, 2), J(2, 6), and K(7, 2) (d) Parallelogram three of whose vertices are L(3, 1), M(9, 1), and P(5, 5) 12.53. Find the area of ^DEF, whose vertices are D(0, 0) and (a) E(6, 4) and F(8, 2); (b) E(3, 2) and F(6, 4); (c) E( 2, 3) and F(10, 7). (12.20) (c) B(0, 8) and C( 5, 8) (d) B(0, 8) and C( 5, 12) (e) B(6, 2) and C(7, 0) (f) B(6, 5) and C(10, 0) (12.19) (12.19)
CHAPTER 12 Analytic Geometry
12.54. Find the area of a triangle whose vertices are (a) (0, 0), (2, 3), and (4, 1); (b) (1, 1), (7, 3), and (3, 6); (c) ( 1, 2), (0, 2), and (3, 1). (12.20) 12.55. The vertices of ^ABC are A(2, 1), B(8, 9), and C(5, 7). (a) Find the area of ^ABC. (b) Find the length of AB. (c) Find the length of the altitude to AB. (12.20) 12.56. Find the area of a quadrilateral whose vertices are (a) (3, 3), (10, 4), (8, 7), and (5, 6); (b) (0, 4), (5, 8), (10, 6), and (14, 0); (c) (0, 1), (2, 4), (8, 10), and (12, 2). 12.57. Find the area of the quadrilateral formed by the lines (a) x (b) x (c) x 0, x 0, x 3, x 5, y 7, y 5, y 0, and y 2, and y 3, and y 6 5 8 (d) x (e) y (f) y 0, x 0, y 0, y 6, y 4, y 6, y 0, and y x, and y 2x, and y x x 2x 1 4 6 (12.21) (12.19)
12.58. Prove each of the following with analytic geometry: (a) A line segment joining the midpoints of two sides of a triangle is parallel to the third side. (b) The diagonals of a rhombus are perpendicular to each other. (c) The median to the base of an isosceles triangle is perpendicular to the base.
(d) The length of a line segment joining the midpoints of two sides of a triangle equals one-half the length of the third side. (e) If the midpoints of the sides of a rectangle taken in succession are joined, the quadrilateral formed is a rhombus. (f) In a right triangle, the length of the median to the hypotenuse is one-half the length of the hypotenuse.