Geometry Questions

owing equation represents a hyperbola Fut the equation in to standard for Standard form of a hyperbola 25x 16y 100x 96y 444 B 11 Based on the equation you just put in to standard form make a conjecture as to where the center is located and how the a and values affect happens to the hyperbola if the x term is negative graph of the hyperbola What 12 Using a graphing utility like Desmos or GeoGebra graph the equation of the hyperbola am confirm your conjectures If necessary make a new conjecture based on your findings aft graphing 13 The transverse axis of a hyperbola connects the two vertices List the coordinates of th vertices

Select the correct answer from the drop down menu How does extending vertex A further to the left of vertex B verify the relationship between sides and angles in t A B As the length AB increases the measure of ZC decreases increases stays the same

Y sec x 1 y tan x y N y 3x 2 1 YOOOL 3 2 2x R Y 4 3 x 2 7 2 3A 4 JUDUL 3 2 R 2 A 3x 2 1 2 91 J2 2 2x X 2x X No the functions are equivalent except when tan x nit 2 JU U VL 3 2 3A 3A nit No the functions are equivalent except when sec x 1 7 YANG 3 2A 2 27 R 3 A 2 y JUUL y y H Use the graphs to determine whether the expressions are equivalent Verify the results algebraically O Yes the expressions are equivalent 2 1 2 3x 2 27 2x

Date Name Read and respond to each question carefully Show work for full points Test is scheduled for Thursday October 5th 2023 tentative 1 Find the length of XY Explain how you found your answer 6 12 2 Point Mis between points L and Non LN LN 6x LM 4x 8 and MN 27 Use the information 6x Use the diagram 3 Give another name for line S 4 Name three points that are coplanar 5 Name three points that are collinear 6 Give another name for plane K 4 2 4x 8 2 2 M 27 7 Plot the points in a coordinate plane Then determine whether AB and CD are congruent 3 2 R Period P 8 The endpoints of CD are C 1 6 and D 7 5 Find the coordinates of the midpoint M 9 The midpoint of RS is M 1 2 One endpoint is R 6 6 Find the coordinates of endpoint S

You will experimentally verify the relationship between side lengths and angles in triangles using geometry software Directions Read the instructions for this self checked activity Type in your response to each question and check your answers At the e of the activity write a brief evaluation of your work Activity Use GeoGebra to explore side angle relationships in triangles and to complete each part For help watch this short video about using GeoGebra measurement tools Part A Use the distance or length tool to add side lengths to the triangle Then use the move tool to drag vertex C to make it the largest angle and then the smallest angle What happens to the side opposite vertex C when it is the largest angle The smallest angle Type your answer in the box

hot tub on e located at ot tub so it is d your Example 3 A is the incenter of APQR Find each measure 7 MZARU P 8 AU 10 mZPHU 11 HU 3x 2 T 20 A 4x 9 40 U is the incenter of AGHY Find each measure 9 MZUGM K R G M 28 H 21 B 12 5 P

Examples 1 and 2 Find each measure 1 mLABE B A 20 E 43 mZEWL W 7 C 7x 5 3x 21 E R 2 mZYBA B 5 IU 19 19 47 8 A 8 T 2x 5 U 7x 3 MK M 2x 13x8 6 mZMYW T 4x 1 Y M 2x 5 W

d x x y 4 Donnie still holds to his claim that this shape is both a parallelogram AND more specifically a rectangle too Except Donnie found a different way to prove this is a rectangle He claims that if the diagonals of the figure are congruent to each other that would prove it s a rectangle Use the distance formula or Pythagorean Theorem to find the length of each diagonal AC and BD Show all work 4 pts 5 Length of AC 4 4 a b c Length of BD a Is Donnie correct Are the diagonals of the quadrilateral congruent 1 pt b If the diagonals are congruent does this make the shape a rectangle a parallelogram or both In other words what shape has congruent diagonals Explain your answer thoroughly 2 pts 6 Why do you think Walter may have thought this was a parallelogram if he was looking at the coordinate plane Does it appear that ABCD has any right angles Explain what s wrong with the diagram that caused Walter to believe this was only a parallelogram 3 pts

5 Using visual observation determine whether the graph is symmetric with respect to the a x axis b y axis or c the origin a is the graph symmetric with respect to the x axis Choose the correct answer below A MO C No because for 2 3 No because for on the graph OB Yes because if a b is on the graph then so is a b the point 1 3 NH the point 3 is not JU 3 is not on the graph OD Yes because if a b is on the graph then so is a b 21 8 2

Give the slope and the y intercept of the line 6x 2y 8 0 Slope y intercept 0

ationalize the denominator just numbe 9 please Evaluate using exact values and rationalize the denominator 25 sin 26 cos 4 Cos 77 5m 6 5m 4 27 2 cos sin 4 28 4sin sin cos 7m 4x 247 3 30 2 cos 29 2 sin 31 sin 5m 32 6 cos 2 r sin 1 11 z 5m cos 1 3 ST cos 117 3 cos

Select the correct choices that complete the sentence below The value of tan 150 is exact value of tan 150 is because 150 is in quadrant The reference angle is

Find the area of the triangle below Carry your intermediate computations to at least four decimal places Round your answer to the nearest hundredth 5 ft 38 7 ft X

Consider a triangle ABC like the one below Suppose that a 53 b 6 and c 54 The figure is not drawn to scale Solve the triangle Carry your intermediate computations to at least four decimal places and round your answers to the nearest tenth If there is more than one solution use the button labeled or 0 B C 0 OF E X No solution

ngle below Carry your intermediate computations to at least four decimal places Round your answer to the nearest hundredth Find the area or 13 in 140 8 in in X

Tom is on vacation at a tropical bay that has three islands He rents a boat on Island A and plans to navigate to Island C which is 15 miles away Based on t figure below at what angle 8 should he navigate to go to Island C Island A B 15 miles 11 miles X 8 miles Island B Island C Carry your intermediate computations to at least four decimal places Round your answer to the nearest tenth of a degree S

Bob is flying two kites He has 98 feet of string out to one kite and 116 feet out to the other kite The angle formed by the two strings is 29 as shown in the figure below Find the distance between the kites 98 ft feet 116 ft Carry your intermediate computations to at least four decimal places Round your answer to the nearest tenth of a foot 29 X S

Write the coordinates of the vertices after a reflection over the line y 1 10 8 6 TOO U 0 v 4 2 10 8 6 4 2 2 4 618 6 W 8 10 2 4 9 6 ND T 80 U 10

In the diagram below PW 6 and WX 4 Find QX X W P

point Each graph below is the graph of a system of three linear equations in three unknowns of the form Az b Determine whether each system has a solution and if it does the number of free variables A choose D choose 8 choose choose choose F choose

In the figure below mJKM 92 KL bisects JKM and KN bisects LKM Find mZMKM m2NKM

Extra Practice In Exercises 1 4 classify the polygon by the number of sides Tell whether it is convex or concave 3 TODO 1 2 4 In Exercises 5 8 find the perimeter and area of the polygon with the given vertices 5 X 2 4 Y 0 2 Z 2 2 6 P 1 3 Q 1 1 R 4 2 7 J 4 1 K 4 2 L 6 2 M 6 1 8 D 5 3 E 5 6 F 2 6 G 2 3

1 4 Notetaking with Vocabulary continued In Exercises 9 14 use the diagram 9 Find the perimeter of AABD 10 Find the perimeter of ABCD 11 Find the perimeter of quadrilateral ABCD 12 Find the area of AABD 13 Find the area of ABCD 14 Find the area of quadrilateral ABCD D 4 1 C 1 5 Ay 2 A 2 4 4 x B 2 1

18 Do you remember the daisy construction from Chapter 0 Construct a circle with radius s With the same compass setting divide the circle into six congruent arcs Construct the chords to form a regular hexagon inscribed in the circle Construct radii to each of the six vertices What type of triangle is formed What is the ratio of the perimeter of the hexagon to the diameter of the circle

11 In the figure at right what is mPQ mPRQ La bas To Tadil TOW sigasi Poel sit com c 12 Use your compass and protractor to make an arc with measure 65 Now make an arcuri 110 with measure 215 Label each arc with its measure O 13 Name two places or objects where concentric circles appear Bring an example of a set of concentric circles to class tomorrow You might look in a magazine for a photo or make a copy of a photo from a book but not this book 14 Sketch two circles that appear to be concentric Then use your compass to construct a pair of concentric circles R e

9 Sketch the path made by the midpoint of a radius of a circle if the radius is rotated about the center

20 Earth takes 365 25 days to travel one full revolution around the Sun By approximately how many degrees does the Earth travel each day in its orbit around the Sun 21 Earth completes one full rotation each day making the Sun appear to rise and set If the Sun passes directly overhead by how many degrees does its position in the sky change every hour

25 A 38 40 a 9 72 m b 11 8 m

24 C 68 5 c 258 cm b 386 cr

13 A 29 7 b 41 5 ft a 27 2 ft

23 B 72 2 b 78 3 m c 145 m

J B 74 3 a 859 m b 783 m

Respond to each of the following a Explain why Figure A is not the image of Figure B after a rotation about point P B B P A b Explain why Figure B is not the image of Figure A after a reflection across line l A

left 2 Select all the sequences of transformations that could map Figure X onto N Y O X A a single translation B a single reflection C a single rotation D a reflection then a different reflection E a translation then a reflection X

Use the given E 1 F H Statement G J K Given EF JK FG HJ Prove EG HK Reason Send To Proof Send To Proof Send To Proof

3 For which pair of figures can Figure Y a Pair 1 b Pair 2 A c Pair 3 Z A Pair 1 B B Z joue beenwoh etinu ewol s syslane T O 4 Refer to the three pairs of figures shown For each pair of figures determine which single transformation translation rotation or reflection maps Figure A onto Figure B C M Z Pair 2 B sagrit to main Shoillaog A hupit s toolog A iubit alsio 8 ods Balvolbolo Pair 3 00 A B

5 Draw the image of the quadrilateral shown after a 180 clockwise rotation about point al pupil vow nislax P

graph of the function y 2 was transformed according to the transformations given below resulting in the graph of the function y a z b c for some constants a b and c 1 reflection over the x axis 2 vertical shrink 3 horizontal shift left 4 vertical shift up Eleanor was asked to provide a possible value for a b and c She said a Determine if each of her values are reasonable and give reasons for your answers 10 Using the graph of g x shown sketch the transformation g x 2 on the same coordinate grid 4 4 43 1 5 3 O M b 4 and c 7 2 3 4 10

Which of the following is true 1 2 B C 70 A m BCD mzDBC 10 B m BCD m DBC 20 C m BCD m DBC 60 D m BCD m DBC 80 130 D

Write an inequality in slope intercept form from the linear inequality graphed below y 10 10 8 64 2 8 6 4 2 24 008 8 4 6810

144 5 4 56 3 2 m 1 m42 m43 m24 m25

The owner of a convenience store installs two security cameras represented by points C1 and C2 Both cameras point towards the centre of the store s cash register represented by the point R The following diagram shows this information on a cross section of the store 2 8 1 0 6 4 diagram not to scale C2 3 1 The cameras are positioned at a height of 3 1 m and the horizontal distance between the cameras is 6 4 m The cash register is sitting on a counter so that its centre R is 1 0 m above the floor The distance from Camera 1 to the centre of the cash register is 2 8 m Determine the angle of depression from Camera 1 to the centre of the cash register Gi

The diagram below shows a helicopter hovering at point H 380 m vertically above a lake Point A is the point on the surface of the lake directly below the helicopter helicopter 380 H 40 B 25 diagram not to scale Minta Minta is swimming at a constant speed in the direction of point A Minta observes the helicopter from point C as she looks upward at an angle of 25 After 15 minutes Minta is at point B and she observes the same helicopter at an angle of 40 a Write down the size of the angle of depression from H to C

the IB SL formula booklet Round to 3 s f if not otherwise specified 21 A garden includes a small lawn The lawn is enclosed by an arc AB of a circle with centre O and radius 6 m such that AOB 135 The straight border of the lawn is defined by chord AB The lawn is shown as the shaded region in the following diagram diagram not to scale 135 ing cal B a A footpath is to be laid around the curved side of the lawn Find the length of the

For Exercises 2 9 use the diagram at right Points E P and is the center of the circle 2 Name three chords 3 Name one diameter 4 Name five radii 5 Name five minor arcs 6 Name two semicircles 7 Name two major arcs 8 Name two tangents 9 Name a point of tangency 10 Name two types of vehicles that use wheels two household appliances that use wheels and two uses of the wheel in the world of entertainment H A E B P F C G

1 In the photos below identify the physical models that represent a circle a radius a chord a tangent and an arc of a circle ction tools for Exercises 12 17 18 22 23

11 Triangle EFD was made by reflecting triangle ABC across 12 B 2 24 71 6 2 83 63 4 45 3 00 A B C Name pairs of corresponding angles from triangles ABC and EFD rocponding sides from triangles ABC and EFD then translating E D 3 00 63 4 45 2 24 71 6 2 83 F

K P K M N N 4 Here is quadrilateral KLMN after a rotation around M KLMN and its image degree counterclockwise

17 BLUE FISH F H 6 E 6 B U L 6 18 RECTANGL G R T C 12 did in 19 Imagine using two congruent triangles to create a special quadrilateral as you the investigation a What type of triangles do you need to form a rectangle Explain b What type of triangles do you need to form a square Explain

A birthday party caterer counted the number of juice cups on the table The cups contained different flavored juices and different shaped straws Orange juice Grape juice Heart shaped straw Star shaped straw 2 3 4 6 What is the probability that a randomly selected cup contains a star shaped straw given that the cup contains orange juice Simplify any fractions