Cracking the SAT Subject Test in Math 2, 2nd Edition (A) (B) (C) (D) (E) TRIAXIAL COORDINATES THINKING IN 3D On the SAT Subject Test in Math 2, you may run into a twist on the coordinate plane—a coord[.]
(A) (B) (C) (D) (E) TRIAXIAL COORDINATES: THINKING IN 3D On the SAT Subject Test in Math 2, you may run into a twist on the coordinate plane—a coordinate space A third dimension can be added to the coordinate plane by introducing a third axis (often referred to as the z-axis) that passes through the origin at right angles to both the x-axis and the y-axis While the x- and y-axes define the location of a point in a plane, the x-, y-, and z-axes define the location of a point in a threedimensional space Such a system of three axes is called a three-dimensional coordinate system, a triaxial coordinate system, or a coordinate space Sometimes it’s not called anything at all; ETS will simply show you a diagram of a three-dimensional graph, or a set of triple coordinates, and expect you to understand what you’re seeing The coordinates of a point in three dimensions are given in this form: (x, y, z) The point (3, 4, 5) is located 3 units along the x-axis, units along the y-axis, and units along the zaxis Always check the labels on the axes if you’re given a diagram, because there’s no firm convention about which axis is pictured in which position If you are given two points in 3-D, (x1, y1, z1) and (x2, y2, z2), then the distance, d, between them is given by the following formula: Distance in a Three-Dimensional Space Connect the Dots This formula is equivalent to the Super Pythagorean Theorem: a2 + b2 + c2 = d2 Most of the three-dimensional coordinate questions on the SAT Subject Test in Math 2 require you to calculate a distance between two points in a 3-D coordinate system Just use the formula DRILL 9: TRIAXIAL COORDINATES Try the following questions involving triaxial coordinates The answers can be found in Part IV 14 What is the distance between the origin and the point (5, 6, 7) ? (A) 4.24 (B) 7.25 (C) 10.49 (D) 14.49 (E) 18.00 19 Sphere O has a radius of 6, and its center is at the origin Which of the following points is NOT inside the sphere? (A) (−3, 5, 1) (B) (− 4, − 4, 3) (C) (5, −2, 2) (D) (4, 1, − 4) (E) (2, − 4, −3) 37 A cube is located in the xyz-coordinate system shown above If A is located at (0, 7.071, 5), then which of the following are the coordinates of B? (A) (0, 5, 7.071) (B) (0, 3.536, 5) (C) (3.536, 5, 5) (D) (3.536, 3.536, 5) (E) (7.071, 5, 5) ... This formula is equivalent to the Super Pythagorean Theorem: a2 + b2 + c2 = d2 Most of the three-dimensional coordinate questions on the SAT Subject Test in Math 2 require you to calculate a distance between two points in a... are given two points in 3-D, (x1, y1, z1) and (x2, y2, z2), then the distance, d, between them is given by the following formula: Distance in a Three-Dimensional Space Connect the Dots This formula is equivalent to the Super... Test in Math 2 require you to calculate a distance between two points in a 3-D coordinate system Just use the formula DRILL 9: TRIAXIAL COORDINATES Try the following questions involving triaxial coordinates The answers can be found in Part IV 14 What is the distance between the origin and the point (5,