Coordinate system Questions and Answers

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T6 Prove trigonometric identities using reciprocal identities quotient identities Pythagorean identities sum or difference identities restricted to sine cosine and tangent double angle identities restricted to sine cosine and tangent 1 15 pts Prove 3 of the following identities for all permissible values of the variable Clearly indicate the selected identity and the chosen side State any non permissible values sinx A C 1 cos x cos 8 cote sec8 tan 8 B cot 8 1 sin 0 tan 8 1 cos 0 1 60s sinx tan x cos x CSCX 1 cos x D cot 0

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10 To determine the height of a tree a botanist makes the following diagram What is the height of the tree z

Find the circumference of the circle Leave your answer in terms of 8 yo

Which radian measure is equivalent to 145 O O O 15 32 29 36 36 29 32T 15

What is the value of cos given that 5 4 is a point on the terminal side of 0 4 41 41 4 41 41 5 41 41 5 41

In 15 20 Use the figure in which AWXZ ADFG 15 State the similarity ratio 16 mZZ 17 mZG 18 mZD W 3 37 X 4 Z F 6 10

3 8 X 10 y Z Z 12 14 Z X y 15 12 Z

1 Find m W Round to the nearest hundredth 18

7 In right triangle MJK the hypotenuse is 1 75 times longer than the side opposite accute angle K Find the measure of angle K to the nearest hundredth

6 5 4 6 All solutions require proper format as modelled in class Communication marks as assigned where indicated in the question to evaluate the clarity of the solution Up to TWO communication marks for proper mathematical formatting Knowledge and Understanding 1 Determine the coordinates of the midpoint of each line segment a J 0 2 1 5 and K 3 6 0 2 1 5 3 5 2 marks

In 6 Given the preimage and image state the coordinates of each figure and the scale factor of the dilation with center at origin Answer in simplest fraction form 6 10 6 8 4 2 O A D 2 A D 4 B C 6 8 10 A A Scale Factor B B C D D

Solve each proportion round answers to the nearest tenth 5 3 6 1 12 7 2 8 x 3 3 x 8 6 x 1 4

In 4 5 describe the dilation and state the scale factor Solid is preimage 4 5 12 cm 3 cm 8 in 6 in 20 in 15 in

9 Graph Quadrilateral MNPQ M 1 3 N 3 3 P 2 3 Q 1 3 then state the coordinates and graph the image after a dilation with a scale factor of 3 using the origin as the center M N P Q

A A 3 0 2 4 12 10 B 6 20 18 A B 2 Ja Factor 6 B B G B 10 12 14 C 16 C 18 20

2 y x 2 5 4 3 2 1 4 4 y x 4 54 3 2 1 6 y 4 3 2 1 7 2 Ay 2 A X XY

A Stop 1 81 hard

y 23 Hanna Anguiano CA Geometry B Illuminate Credit 1 pdf Your Turn Show that each quadrilateral is a parallelogram for the given values of the variables Step 2 is done for you 1 z 11 and w 4 5 Step 1 Find LF and LH So mZF m and mZE m 9z 19 12w 8 Step 2 Find LE and LG 14w 1 11z 3 LE 12 4 5 8 54 8 EFGH is a parallelogram since 62 LG 14 4 5 1 63 1 62 H 100 G

Use the DESMOS software to complete the following questions 1 Complete the table below by graphing using DESMOS software Vertex y x 5 y x 2x 3 x 2x 3 y 2x 5x 3 y 2x 4x 7 Direction of opening Maximum Minimum Axis of symmetry x intercepts y intercept

A O Qo B Suppose that line segment A B is the image of line segment AB after a dilation with a scale factor of 0 5 centered at point Q Write a statement that best describes the position of line segment A B AIR 2 The image shown will undergo a dilation centered at point B with a scale factor of 2 Which lines will not be changed by the transformation tornan ed H 3 In the coordinate plane quadrilateral ABCD has vertices A 1 1 B 5 1 C 5 9 and D 1 9 Quadrilateral FGHJ is shown in the coordinate plane to the right What are the scale factor and the center of dilation that map quadrilateral ABCD onto quadrilateral FGHJ AUCH 35 BOK U B 9 10 4 Under a dilation where the center of dilation is the origin the image of X 3 4 is X 9 12 What are the coordinates of Y the image of Y 5 0 under the same dilation 171

11 x 1 X

X Alu x 2 4

7 93 x 1 5 8 8 3 9 x 3 5 3 9 X x 1

Solve each proportion for the variable round answers to the nearest tenth 9 2 1 X 4 3 11 y 14 21 3 56 6 618

For each rectangle write the ratio of the longer side to the shorter side Simplify if possible 1 70 ft 25 ft 2 12 cm 18 cm 3 36 in 21 In

Trigonometry ASSESSMENT Credit Checkpoint Complete the following problems Show all your work Round all side lengths to the nearest tenth and all degrees to the nearest degree When applicable leave your answers in radical form How I Did Circle one I got it Learning Goal from Lesson 13 1 and 13 2 I can explain how to derive the trigonometric ratios for acute angles 1 Name the following sides of the triangle 1 point a Opposite Leg of ZA b Adjacent Leg to ZA bu A N B 2 Write an equation that can be used to find mzM Then solve it Round to the nearest degree 1 point 5 I m still learning it 11 M

If AB DE and AC DF which statement does NOT allow you to conclude that AABC ADEF A BC EF B LA LD C ZA and ZD are right angles D LB LE yriw nislaxs of beau 9d 60 me10ert w woladelgmsmit no bez B F menosdT asignA 9268 A C E 643

11 The scalar projection of a onto b is 8 If the length of a is 11 then what is the angle to the nearest degree between a and b

coordinates 10 8 6 4 2 R S S R 104 8 6 9 4 2 2 4 6 8 10 2 4 ection over the x axis T 6 U 8 X 10

1 Follow the steps below to help you prove or disprove that the point 1 15 lies on the circle that is centered at the origin and contains the poin 0 4 To earn full credit you must show your work Step 1 Plot a point at the origin and at 0 4 Use these to help you draw the circle centered at the origin that contains 0 4 Step 2 Determine the radius Step 3 Use the radius and the coordinates of the center to write the equation of the circle Step 4 Substitute the x and y coordinates of the point 1 15 in the equation of the circle to check whether they satisfy the equation

RMV MVR Addition Property of Equality Vertical Angles Theorem Alternate Interior Angles Theorem Prove Find the measure of RMV Statement 1 FARM is a parallelogram m AFV 42 m FVA 117 2 FM AR 3 ZAFV ZMRV 4 m MRV 42 5 LFVA 6 mzMRV m2MVR mzRMV 180 7 42 117 m RMV 180 8 159 m RMV 180 Justification 1 Given 2 Property of Parallelogram 3 4 Transitive Property 5 Vertical Angles Theorem 6 Triangle Sum Theorem 7 Substitution 8

Question 1 Consider the Triangle XYZ Y 1 3 2 1 0 N T Z 1 4 3 4 5 6 X 4 2 Triangle XYZ is reflected over the y axis to create X Y Z and then translated by the rule x y x 4 y 3 to create X Y Z Write the coordinates for Triangle X Y Z and Triangle X Y Z Express your answer as an ordered pair X Y i X Y 7

d all angles and sides of the triangle C 6 95

650 X

4 Convert the expression

Does JM bisect J Explain cmpo 15 M

symm Jennifer draws the rectangle ABCD Find all rotations and reflections that carry rectangle ABCD onto itself

What is the image of the point 5 4 after a rotation of 270 counterclockwise about the origin

Does JM bisect J Explain Nound 15 L 5 M 6

Find the exact value of the expression if possible If not possible enter IMPOSSIBLE a cos arc sin b sin arc tan

19 Find the magnitude and direction angle of v 2i 6j Round the direction angle to the nearest degree O 67 0 279 O v 2 10 0 252 O lv 30 0 239 O v 2 13 0 260 ly l 3 7 A 269

4 Given A 50 B 74 and c 8 use the Law of Sines to solve the triangle for the value of a Round your answer to two decimal places O O A a 7 39 a 6 38 a 8 66 a 6 9 a B

Find the total area of the shaded regions 6 RE 16 x 16x U COB The total area of the shaded regions is Type an integer or a simplified fraction

equation below gives parametric equations and parameter intervals for the motion of a particle in the xy plane Identify the particle s path by finding a Cartesian equation for it Gra Cartesian equation Indicate the portion of the graph traced by the particle and the direction of motion x 5t 6 y 25t o t Find a Cartesian equation for the particle s path 10 y Graph the Cartesian equation below Indicate the direction of motion as t increases Choose the correct graph below OA O C OB 10 10 A TO Q 14 A point s possible This question 4 point s possible Q Indicate the portion of the graph traced by the particle Select the correct choice below and if necessary fill in the answer box to complete your choice A The portion of the graph where t is greater than B The entire graph C The portion of the graph where t is less than OD Sul

Theorem 3 12 Lines Perpendicular to a Transversal Theorem In a plane if two lines are perpendicular to the same line then they are parallel to each other If m 1 p and n 1 p then m n Notes Extra Practice In Exercises 1 4 find the distance from point A to BC Ay 1 3 3 0 A B 4 B 1 3 2 3 4 A 3 3 4 2 Ay 4 C D 0 1 3 2 D 1 2 4 x 2 C 1 1 4 x Use the distance formula for 1 4 2 4 A 3 4 4 2 4 2 Ay 4 2 2 C 1 4 D 0 4 D 3 2 B 4 A 1 3 C Am n FF 4 1 X 3 2 B 1 2 4 x

25 Spiral based on Question 5 2b test Triangle ABC DEF if A x 45 and C 35 and D 60 Then Find A Hint what is true about the angles in congruent triangles

26 Spiral based on Question 10 2b test 6x 7 2x 103 x

X 22 5 x A C B 150 erf anwa asi o rio