Geometry

Coordinate systemE im ve y kesi im noktas n kullanarak her denklemin grafigl 3 15 y x 1 4 yama y int 7 6 5 4 3 2 1 2 3 4 5 8 3 4 5 16 8y 16x 24 E im kesi im formu yama y int 7 5 6 4 3 2 6 5 3 24 2 2 3 5

Geometry

Coordinate system10 To determine the height of a tree a botanist makes the following diagram What is the height of the tree z

Geometry

Coordinate systemWhat 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

Geometry

Coordinate systemIn 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

Geometry

Coordinate system7 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

Geometry

Coordinate system6 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

Geometry

Coordinate systemIn 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

Geometry

Coordinate systemSolve 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

Geometry

Coordinate systemIn 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

Geometry

Coordinate system9 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

Geometry

Coordinate systemA 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

Geometry

Coordinate systemy 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

Geometry

Coordinate systemUse 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

Geometry

Coordinate systemA 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

Geometry

Coordinate systemSolve 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

Geometry

Coordinate systemFor 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

Geometry

Coordinate systemTrigonometry 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

Geometry

Coordinate systemIf 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

Geometry

Coordinate system11 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

Geometry

Coordinate systemcoordinates 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

Geometry

Coordinate system1 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

Geometry

Coordinate systemRMV 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

Geometry

Coordinate systemQuestion 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

Geometry

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

Geometry

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

Geometry

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

Geometry

Coordinate system19 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

Geometry

Coordinate system4 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

Geometry

Coordinate systemFind 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

Geometry

Coordinate systemequation 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

Geometry

Coordinate systemTheorem 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

Geometry

Coordinate system25 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

Geometry

Coordinate systemof congruence to decide if the two figures are congruent Explain your answer Give Coordinate Notation for the transformation you use Question 11 Question 12 N D B E 4 V 4 C 8 8 C D 0 4 8 8