Geometry Questions

A right triangle has legs of length 4 and 16 Use the Pythagorean theorem to find the length of the hypotenuse Express numbers in exact form Use symbolic notation and fractions where needed length of hypotenuse

Macmillan Learning Recall that in a triangle the angle sum is r radians or 180 An equilateral triangle has all three angles equal What is the degree measure of an angle of an equilateral triangle Give an exact answer Use symbolic notation and fractions where needed Include the degree symbol in your answer angle

x 3 In the graph below drag the green x intercept s to the correct position s Drag the red vertical asymptote s to the correct position s Drag the two orange points to form the correct slant asymptote Determine several points of the function and drag the blue point to one of these locations Choose a point that is not an x intercept and for which the y coordinate is a multiple of 0 1 Otherwise you won t be able to drag the blue poir to the exact location When finished click CHECK 10 6 2 5 10 5 I 10

The graph of f x 2 13x 54x 72 is given below Use the graph of f to solve the following equation r 13x 54x 72 0 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 8 9 2 3 7 8

Determine the perimeter of given figure on th coordinate plane Round your answer to the nearest hundredth if necessary Figure ABCDEF A YA F 86 4 2 B 8 0 O 8 6 4 22 LE 6 8 C 2 4 6 8 D AX

Prob 1 3 General Addition Rule Set backpound Clear fame Complete each probability model by finding the probability of B only Warm up Shade the region that represents the union on the two events A or B Then momote tha nenhahility A 0 25 B A 0 05 B

Show how each vertex of AEFG maps to its image Describe in words how to map AEFG to its image AE F G using a reflection 6 V G 4 R A fu Ay 10 8 6 4 2 2 4 6 101 Complete the table with the coordinates of the image points E F and G AEFG 4 5 2 5 3 2 E F G Type ordered pairs E F G AE F G

Given AXYZ ARST find the values of a and b N 5b 3 70 4a 4 R 62 T 48

3 4 Angles 4 5 and 6 are in the ratio 2 5 3 Find the measure of each angle 4 5 Find m 1 1 6 x 8 2x

Y 2 Z 16 reflection across the x axis P y W y 18 reflection across the y axis Ay 10 X Boisinuos D doijet X X

20 rotation 900 origin D siter H 22 rotation 180 about the origin B Ay W T G y X H X 24 rotation 180 about the origin X orli 32010 OTSE

B A F S N H 10 translation 2 units right and 5 units down Y Z X S P 12 translation 4 units right and 1 unit up Atel X rli joods 081 XY

2 dilation of 2 5 6 4 reflection across the y axis R J F A H F R W y N X X

10 5 TT VE 10 0 5 is 5 X 10 A triangle on the coordinate plane has points located at A 1 6 B 4 3 and C 1 1 What is the area of the triangle I Submit of 9

2 G GSR 5 2 The accompanying diagram shows two similar triangles A C dant X Which proportion could be used to solve for x 32 12 x 9 15 x 24 32 15 12 x 32 B D 24 9 9 24 15 15 X 12 15

20 A cross section of which of the following would show dark edges and brighter center when viewed in transmission mode with a MSP A B C D pr Round Carugo 10h 11 Flat Trilobal 8 en quant

3 For Andrew s graph write a next to the 1st and 2nd transformations in the sequence of transformations represented by his graph Not all choices will be used a Dilation by a scale factor of b Rotation 90 clockwise c Translation 6 units up d Dilation by a scale factor of 4 e Translation 6 units left 5 Ricardo will transform a triangle contained in quadrant II by reflecting over the x axis and dilating by a scale factor of 0 5 Which is not a true statement A The image will be in quadrant III B The orientation of the vertices will change C The orientation of the figure will change The image will be congruent to the

20 tan 22 tan tane 90 Y 24 tan 0 X 0 270 90 undifined Ne saution 30 21 sin 0 23 cos 25 tan 780 780 360 510 2 Que V 120 costo x 1 360V 60 X 810 3 81c 8 10 TO 366 958 860 40 und

14 140 Le 18 tan Find the exact value of each trigonometric function Create a right triangle lable all angles and find the sides of that triangle using sin cos tan cost 16 cos 17 cos 0 2 600 150 15 2 Fan 150 2 2 10 100 19 cos 450 870 450 360 40 cas

Line segment m has a length of 5 What is its length after each dilation Type the correct answer in each box Use numerals instead of words Round any decimal answers to the nearest hundredt For help see this worked example scale factor of 2 centered at the origin scale factor of 10 centered at the origin scale factor of 0 25 centered at the origin h

3 Student response use the graph to respond to each question Justify y 21 3x 1 y x 3x 1 X X a Identify the functions as a or b 5 10 J b From the graph determine the solution set explain c Solve the system of equations algebraically 10

X W 35 Z 4x 7

Measure and record the slopes of these line segments in the original logo Then set n 0 5 and n 2 and record the slopes of the corresponding line segments in each resulting image BIUX X 14pt E V AVA Line Segment Original Slope Slope After Dilation n 0 5 LK GB AH n 2 Space used includes formatting 1008 15000

Example 1 Consider the graph G given in Fig 1 15 2 1 2 Subgraph H 3 4 Spanning Subgraph 1 Subgraph of G Fig 1 19 5 5 G Fig 1 16 3 Fig 1 15 2 4 b b 3 3 Fig 1 17 Fig 1 18 Example 2 Consider the Peterson graph G given in Fig 1 4 5 Co a a Ve 13 Subgraph H 3d d 4 Induced subgraph of G Fig 1 20 e 5 5 Induced Subgraph Fig 1 4 5 Fig 1 21 Spanning Subgraph of EXI be e 3

Street C is perpendicular to Street A and passes through 4 6 Write this street s equation in standard form

Measure and record the lengths of these line segments in the original logo Then set n 0 5 and n 2 and record the lengths of the corresponding line segments in each resulting image BIY X X 14pt E Line Segment 13 1814 LK GB AH Original Length Space used includes formatting 954 15000 6 38 Length After Dilation n 0 5 n 2

The expression simplifies to an u 1 cos u 1 cos u X sin u cos u cos 2

In general how do the slopes of line segments in the image compare with the slopes of corresponding line segments in the preimage What effect does the scale factor of the dilation have on the slopes if any BIVX X 15px E

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Question Describe a sequence of transformations that takes Figure Q to Figure P 4 3 Q 2 1 2 1 0 1 1 2 3 P 4 5 6 Describe a sequence of transformations that takes Figure Q to Figure P Skip Question Scratch Paper Optional To Use Functions 7 Previous Question 4 8 5 S 2 AC 9 6 X F

The graph below shows the height of a burning candle over time Height of candle cm 10 Time Hours Question After how many hours will the height of the candle be zero otion road aloud After how many hours will the height of the candle be zero Explain how you figured out when the height of the candle will be zero Skip Question Scratch Paper Optional To Use Previous Question Functions 7 8 4 51 AC 9 6 x 1

A dilation with center P and scale factor 2 is applied to triangle ABC A 45 3 B Question What is the length of the image of segment AC under this dilation What is the length of the image of segment AC under this dilation Skip Question Scratch Paper Optional To Use I Functions 7 4 1 Previous Question 0 8 5 2 AC 9 6 3 11 X

Ava is 60 inches tall Jeremy is 25 taller than Ava This Question How tall is Jeremy How tall is Jeremy Skip Question Scratch Paper Optional To Use Functions 7 4 1 Previous Qu 0 8 5 2 AC 9 6 3

Ruben knows triangle ABC and triangle DEC are similar B 43 C E uestion What is the measure of angle DCE What is the measure of angle DCE Skip Question Scratch Paper Optional To Use Functions 7 4 Previous Questi 1 8 AC 5 6 2 3

Figure ABCD is a square 2 B Question What is the area of ABCD here if you would like to hear this question read aloud What is the area of ABCD Skip Question Scratch Paper Optional To Use Functions 7 4 1 Previous Question 0 8 5 2 AC 9 6 3 11 X 1

A scale drawing of a rectangular park is 8 inches long and 5 inches wide The rectangular park is 320 feet long in real life 8 inches inches Scale drawing 320 feet Real life park Question What is the area of the rectangular park in real life What is the area of the rectangular park in real life What are the units of your answer I Skip Question Scratch Paper Optional To Use Functions 7 Previous Question 1 8 LO 2 AC 9 6 3 X I

The square ABCD is reflected over the y axis then translated one unit to the left to make the square A B C D 5 4 A D B C 1 3 0 1 2 3 4 6 1 2 3 4 Question If the original coordinate pair for point A is 4 1 what is the coordinate pair of A If the original coordinate pair for point A is 4 1 what is the coordinate pair of A Skip Question Scratch Paper Optional To Use I Functions 7 4 1 Previous Question 0 8 5 2 AC 9 6 3 X

A pizza restaurant sells a small square pizza 5 inch side length for 4 The pizza restaurant also sells a large square pizza with a 12 inch side length 5 inches 5 inches 12 inches 12 inches Question What should the cost of a large square pizza 12 inch side be so that both pizzas cost the same amount per square inch Click here if you would like to hear this question read aloud What should the cost of a large square pizza 12 inch side be so that both pizzas cost the same amount per square inch Skip Question Scratch Paper Optional To Use Functions 7 1 Previous Question 0 8 5 2 AC 9 x 6 3

Data was collected on housing prices in a local neighborhood Point A represents a mansion that a movie star lives in Frequency 0 1 x 125000 X XX XX XXX x X xx XXXX XX XXXXXXXXXXXXX XXXXXXX XXXXXXXX 250000 375000 500000 Home Price 625000 Click here if you would like to hear this question read aloud Point A 750000 X 875000 Question If point A is removed from the data set what would happen to the mean If point A is removed from the data set what happens to the mean of the data set Increase Skip Question Scratch Paper Optional To Use Decrease Functions 7 4 1 0 Previous Question 8 5 Stay the same 2 AC 9 6 3 X

A bouncy ball will bounce 80 of the height it falls If a bouncy ball is dropped from 20 feet the first bounce will be 16 feet high The second bounce will be 12 8 feet high Question What will be the height of the third bounce What is the height in feet of the 3rd bounce of the supe ball Skip Question Scratch Paper Optional To Use Functions 7 4 1 Previous Question 0 8 5 2 AC 9 6 3 11 x

The sun creates shadows for Julian and a nearby tree Julian is 5 feet tall and his shadow is 4 feet long At the same time a tree has a shadow that is 10 feet long A 4 ft 5 ft 10 ft Question What is the height of the tree Click here if you would like to hear this question read aloud What is the height of the tree Skip Question Scratch Paper Optional To Use Functions 7 4 1 Previous Question 0 8 5 2 AC 9 6 3 X

Question Write an equation that represents the graph of the linear function below Click here if you would like to hear this question read aloud Write an equation that represents the graph of the linear function below Skip Question Scratch Paper Optional To Use Functions 7 4 1 0 8 5 2 AC 9 6 3 X

Question What number goes in the blank to make this number sentence true 27 15 30 Click here if you would like to hear this question read aloud sentence true Skip Question Scratch Paper Optional To Use I Functions 7 4 1 Previous Question 0 8 01 5 2 AC 9 6 3 x T

Question Solve the equation below for x 1 6 7x 1 5 2 Skip Question Scratch Paper Optional To Use Functions 7 4 Previous 1 8 LO 5 2

Solve for the value of b 6b 7 7h 8

Solve for the value of a 50 8a

Solve for the value of n 37

Solve for the value of v 50 v 7

A sandbox is being built in a park The diagram shows the four vertices of the sandbox Each unit in the coordinate plane represents 2 fee Find the area of the sandbox 20 16 12 8 4 5 12 4 8 14 12 14 8 12 16

Solve for the value of q 59 5 49 5