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Lesson 6 Menu

Determine whether the dilation is an enlargement , reduction , or congruence transformation for a scale factor of r= 2/3. Determine whether the dilation is an enlargement , reduction , or congruence transformation for a scale factor of r = 24.

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Lesson 6 Menu

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  1. Determine whether the dilation is an enlargement, reduction, or congruence transformation for a scale factor of r= 2/3. • Determine whether the dilation is an enlargement,reduction, or congruence transformation for a scale factor of r = 24. • Determine whether the dilation is an enlargement,reduction, or congruence transformation for a scale factor of r = 1. • Find the measure of the dilation image of AB with the scale factor r = – 2 and AB = 3. • Find the measure of the dilation image of AB with the scale factor r = 5/7 and AB = 3/5. Lesson 6 Menu

  2. Find magnitudes and directions of vectors. • Perform translations with vectors. • vector • equal vectors • parallel vectors • resultant • scalar • scalar multiplication • magnitude • direction • standard position • component form Lesson 6 MI/Vocab

  3. Lesson 6 KC1

  4. Write the component form of . Write Vectors in Component Form Lesson 6 Ex1

  5. Write Vectors in Component Form Find the change of x values and the corresponding change in y values. Component form of vector Simplify. Lesson 6 Ex1

  6. Write the component form of . A. B. C. D. • A • B • C • D Lesson 6 CYP1

  7. Find the magnitude and direction of for S(–3, –2) and T(4, –7). Magnitude and Direction of a Vector Find the magnitude. Distance Formula Simplify. Use a calculator. Lesson 6 Ex2

  8. Graph to determine how to find the direction. Draw a right triangle that has as its hypotenuse and an acute angle at S. Magnitude and Direction of a Vector Lesson 6 Ex2

  9. tan S Magnitude and Direction of a Vector Substitution Simplify. Use a calculator. Lesson 6 Ex2

  10. A vector in standard position that is equal to forms a –35.5° degree angle with the positive x-axis in the fourth quadrant. So it forms a angle with the positive x-axis. Answer: has a magnitude of about 8.6 units and a direction of about 324.5°. Magnitude and Direction of a Vector Lesson 6 Ex2

  11. Find the magnitude and direction of for A(2, 5) and B(–2, 1). • A • B • C • D A. 4; 45° B. 5.7; 45° C. 5.7; 225° D. 8; 135° Lesson 6 CYP2

  12. Lesson 6 KC2

  13. Graph the image of quadrilateral HJLK with vertices H(–4, 4), J(–2, 4), L(–1, 2) and K(–3, 1) under the translation of . Next translate each vertex by , 5 units right and 5 units down. Translations with Vectors First graph quadrilateral HJLK. Answer: Connect the vertices for quadrilateral H'J'L'K'. Lesson 6 Ex3

  14. Graph the image of triangle ABC with vertices A(7, 6), B(6, 2), and C(2, 3) under the translation of A.B. C.D. • A • B • C • D Lesson 6 CYP3

  15. Lesson 6 KC3

  16. Graph the image of ΔEFGwith vertices E(1, –3), F(3, –1), and G(4, –4) under the translationand . Translate ΔEFG by a. Then translate this image of ΔEFGby b. Add Vectors Graph ΔEFG. Method 1Translate two times. Translate each vertex 4 units left and 2 units up. Then translate each vertex of 2 units right and 3 units up. Label the image ΔE'F'G'. Lesson 6 Ex4

  17. Add a and b. Add Vectors Method 2Find the resultant, and then translate. Translate each vertex 2 units left and 5 units up. Answer: Notice that the vertices for the image are the same for either method. Lesson 6 Ex4

  18. Graph the image of ΔABCwith vertices A(0, 6), B(–1, 2), and C(–5, 3) under the translation by and A.B. C.D. none of the above • A • B • C • D Lesson 6 CYP4

  19. Lesson 6 KC4

  20. Solve Problems Using Vectors A. CANOEING Suppose a person is canoeing due east across a river at 4 miles per hour. If the river is flowing south at 3 miles an hour, what is the resultant direction and velocity of the canoe? The initial path of the canoe is due east, so a vector representing the path lies on the positive x-axis 4 units long. The river is flowing south, so a vector representing the river will be parallel to the negative y-axis 3 units long. The resultant path can be represented by a vector from the initial point of the vector representing the canoe to the terminal point of the vector representing the river. Lesson 6 Ex5

  21. Solve Problems Using Vectors Use the Pythagorean Theorem. Pythagorean Theorem Simplify. Take the square root of each side. The resultant velocity of the canoe is 5 miles per hour. Use the tangent ratio to find the direction of the canoe. Use a calculator. Lesson 6 Ex5

  22. Solve Problems Using Vectors The resultant direction of the canoe is about 36.9° south of due east. Answer: Therefore, the resultant vector is 5 miles per hour at 36.9° south of due east. Lesson 6 Ex5

  23. Magnitude of Solve Problems Using Vectors B. CANOEING Suppose a person is canoeing due east across a river at 4 miles per hour. If the current reduces to half of its original speed, what is the resultant direction and velocity of the canoe? Use scalar multiplication to find the magnitude of the vector for the river. Simplify. Lesson 6 Ex5

  24. Solve Problems Using Vectors Next, use the Pythagorean Theorem to find the magnitude of the resultant vector. Pythagorean Theorem Simplify. Take the square root of each side. Then, use the tangent ratio to find the direction of the canoe. Use a calculator. Lesson 6 Ex5

  25. Solve Problems Using Vectors Answer: If the current reduces to half its original speed, the canoe travels along a path approximately 20.6° south of due east at about 4.3 miles per hour. Lesson 6 Ex5

  26. KAYAKING Suppose a person is kayaking due east across a lake at 7 miles per hour. If the lake is flowing south at 4 miles an hour, what is the resultant direction and velocity of the canoe? • A • B • C • D A. Direction is about 60.3° south of due east with a velocity of about 8.1 miles per hour. B. Direction is about 60.3° south of due east with a velocity of about 11 miles per hour. C. Direction is about 29.7° south of due east with a velocity of about 8.1 miles per hour. D. Direction is about 29.7° south of due east with a velocity of about 11 miles per hour. Lesson 6 CYP5

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