Geometry Questions

Question 8 If ACDE were reflected across the line y x what would be the coordinates of ACD E 8 6 4 2 co 6 A 2 2 4 6 14 C 2 6 8 D E

8 6 4 2 A B C D 2 4 6 C 2 4 8 D E x 8 C 1 5 D 8 2 E 7 6 C 1 5 D 8 2 E 7 6 C 1 5 D 8 2 E 7 6 C 5 1 D 2 8 E 6 7

Question 7 Triangle ABC is reflected over the line y 1 to produce triangle A B C 8 6 2 6 4 2 1 2 4 4 2 2 B 6 4 1 8 A

4 Question 4 10 8 6 4 2 Question 4 If ATUV is translated to image ATUV as shown below by the rule z y z 8 y 3 what are the coordinates of ATUV 10 8 96 4 2 2 4 6 9 8 10 Y II Pause Q Zoom T U 2 4 6 8 10 X V

Write the equation of the circle in standard form Then identify its center and radius 9x2 9y2 72x 54y 104 0 Center Radius

Figure 1 B C Figure 2 Saorise claims that there is a sequence of transformations that carries Figure 1 onto Figure 2 Select ALL actions that she could take to justi A show that a rotation of 180 counterclockwise about the origin carries Figure 1 onto Figure 2 show that a reflection over the x axis followed by a reflection over the y axis carries Figure 1 onto Figure 2 show that a translation of 4 units right followed by a translation of 5 units down carries Figure 1 onto Figure 2 show that a rotation of 90 clockwise about the origin followed by a reflection over the x axis carries Figure 1 onto Figure 2 D Pause 5

E 10 8 6 4 2 O E A B C D F 8 co 6 41 G 2 2 A 16 10 2 4 6 8 10 G x y x 4 y 11 x y x 4 y 11 x y r 11 y 4 x y x 11 y 4

Find the standard form of the equation of the parabola with the given characteristics y 10 V 0 0 2 2 2 2

000 8 6 4 2 A A 6 B IMAGE 2 4 61 x 0 x 1 C y 2 PREIMAGE 2 6 8

If AOCD AJAL then which of the following statements are true 1 OC JA II E IV OD AL ZCOD ZAJL ZDCO A B C JAL I only II only I and III

Question 2 A triangle with coordinates A 1 1 B 4 2 C 3 5 is translated three units down and five units to the left What are the coordinates of the new triangle A A 2 4 B 1 3 C 0 0 A 4 2 B 1 1 c 2 2 A 4 2 B 7 3 C 6 0 A 4 2 B 1 3 C 2 6 B C D

Identify the center and radius of the circle x y 3 16 center x y radius

Melissa needs to translate a figure six units to the right and two units down Which of the following rules correctly represents that translation A z y z 2 y 6 z y z 2 y 6 z y 2 6 y 2 x y z 6 y 2 B C D

In Silicon Valley a number of computer firms were found to be contaminating underground water supplies with toxic chemicals stored in leaking underground containers A water quality control agency ordered the companies to take immediate corrective action and contribute to a monetary pool for the testing and cleanup the underground contamination Suppose that the required monetary pool in millions of dollars is given by the following function where x is the percentage expressed as a decimal fraction of the total contaminant removed Complete parts A through E P x 3x 1 x OA The x intercept s is are x Simplify your answer Use a comma to separate answers as needed OB There are no x intercepts Find the y intercept s Select the correct choice below and if necessary fill in the answer box to complete your choice A Simplify your answer Use a comma to separate answers as needed OB There are no y intercepts E Sketch a graph of P x Choose the correct graph below OA OA The y intercept s is are y 0 x 1 APDO 50 0 A Q Q OB APDO 50 14 GEXED Q 12 OC AP X Q LL Q OD 50 APDO Q Q G

4 Assume each outcome in the sample space represented by the Venn diagram below is equally likely Are A and B independent FOB OO O Yes No

Question 3 of 7 3 Assume each outcome in the sample space represented by the Venn diagram below is equally likely Find P AIB A Answer B

Find the center radius form of the equation of the circle described and graph it center 0 2 radius 2 Type the center radius form of the equation of the circle x y 2 Type an equation Simplify your answer Graph the circle 4 Click to enlarge graph 10 Ay 10

8 cm 9 a Given the square based prism shown where AB 3 cm and AE state whether each statement is true or false Explain i AB GH GH b Calculate the magnitude of BD BE and BH H E F CG iii AD DC iv AH BG ii EA ii EA CG G

4 Vectors a b and care as shown a Construct a b 7 b Construct a b 2 c Compare your results from parts a and b

3 Given the vectors a b and 2 construct vectors equivalent to each of the following b 1 7 fo to

2 Given AABC draw appropriate arrows on the sides of the triangle and give a single vector equivalent for each of the following a BC CA b AB BC CA C AB AC d BC BA

1 The vectors and are drawn as shown below Draw a vector equivalent to each of the following X

11 AB is a vector whose tail is at 4 2 and whose head is at 1 3 a Calculate the magnitude of AB b Determine the coordinates of point D on vector CD if C 6 0 and CD AB c Determine the coordinates of point E on vector EF if F 3 2 and EF AB d Determine the coordinates of point G on vector GH if G 3 1 and GH AB

Sketch a picture with the coordinates of the unit circle on the terminal side clearly labeled assuming the given angle is in standard position Use the picture to find the exact value a sin 4 3 b tan 5 se 3 4

3 7 6 5 44 3 2 1 7 6 5 4 3 98 2 1 2 3 6 7 8 9 y 1 2 3 4 5 6 7 X 8 Position the four points so they do not coincide and so they all lie on the graph of the same logarithmic function

Select the true statements to determine whether ADAC is congruent to ABCA B Show your work here ZACBZCAD 46 The triangles are not congruent AB AD C The triangles are congruent by the SAS criterion 46 ZCABZDCA A The triangles are congruent by the AAS criterion The triangles are congruent by the ASA criterion D

Select all true statements C A Show your work here CB BE AB BD 4 6 B 6 4 AB BE ZBACZBDE because vertical angles are congruent CB BD The triangles are congruent by the ASA criterion ZABC ZDBE because vertical angles are congruent The triangles are congruent by the SAS criterion D The triangles are congruent by the SSA criterion E

Draw the image of the triangle under a dilation about the origin with a scale factor of 2 Show your work here 14 12 10 8 6 4 144 12 10 8 6 6 6 8 10 12 13

OP and MN are parallel Select the valid statements used to prove whether APMO is congruent to ANOM Select as many as apply M Show your work here MOOM MN MO P ZNZP 25 ZOMN ZMOP because they are alternate interior angles The triangles are congruent by the AAS criterion The triangles not congruent 25 N O

Determine whether the triangles are congruent Note the triangles are not drawn to scale 8 Congruent 22 28 63 Show your work here 28 8 O Not congruent

Solve for Lc Submit your answer in terms of degrees A B 76

Solve for Za Submit your answer in terms of degrees Show your work here 113 a A B

The two rectangles are similar Find y y 12 ST 5 3

Joyce is building a railroad track that crosses the road at an angle The rails of the track must be parallel The sides of the road are parallel What must be the measure of z 1 124 I

Solve for Zz Submit your answer in terms of degrees 57 A B

Solve for Lc Submit your answer in terms of degrees B Show your work here 63

Are the lines Y and Z parallel The figure may not be drawn to scale Y Z Show your work here 43 137

1 Civil engineering is of immense importance because it plays a crucial role in designing constructing and maintaining the infrastructure that supports society From buildings bridges and roads to dams airports and water supply systems civil engineering ensures the safety functionality and sustainability of our physical environment It contributes to economic growth enhances quality of life and addresses societal needs such as transportation water re

Which name refers to the same line as DB O EA C O P m A Show your work here E B n F P O OF m G D

Solve for x Leave your answer in simplest radical form 2

Find the value of a to the nearest tenth X IC 8

ABCD is a kite so AC 1DB and DE EB Calculate the length of AC to the nearest tenth of a centimeter D 9 cm 8 cm C E 14 cm B

Find the value of x Leave your answer in simplest radical form X 3

b g g h h 41 55 Y 33 8 B a a B Y d

A propery is being transported through a fhuid a steady state through a constant coss sectional area At point the concentration is 278 x 102 amount of property m and 1 50 x 10 at point 2 at adistance of 20 m away Thedificivity depends on concentration as 80150 14651 a Calculate the steady state fua if the two points were separated by 35 m but with the same concentrators How does the flux vary with the distance between the points Calculate the steady state flux if the concentration at point 2 was 150 x 10 amount of property using the nigral disance 2 0 m How does the way with th diference in concentration b

4 Use the given information to determine the remaining five trigonometric values a Sin A 4 4 7 b 7 b tan A 2 1 2 1 2 1 2 1 H A

5 Verify each equation a cos 60 1 2sin 30 b sin 30 1 cos 600 2

2 Let 0 be an acute angle Complete the following table 0 30 45 60 sin 0 COS A tan 0

4 Suppose is an acute angle and cos B find sin and tan Two ways to do this b 4 B 7 OR

Find the values of the six trigonometric functions of 0 adj 8 sin cos tan 0 0 17 hyp a 15 opp csc sec cot 0 a 8 17 a 64 289 a 225 a 15