Geometry Questions

4 1 8 Triangle ABC has vertices A 1 3 B 0 1 and C 4 0 Under a translation A the image point of A is located at 4 4 Under this same translation point C is located at

6 translation x y x y 4 y R S Q X

12 reflection across y 1 D E X

10 translation x y x 1 y 2 Ay H X

11 reflection across y 1 T U y X

3 reflection across the y axis Y y X

3 reflection across the y axis Y X

4 reflection across the x axis y F X

A 3 C 5 4 W B Z Y Triangle ABC is similar to triangle WYZ 3 Select all angles whose cosine equals 5

C 26 True False 12 B W 5 Z Triangle ABC is similar to triangle WYZ Determine whether the following statement is true or false sin B sin Y

the length of AB Round to the nearest hundredths place C 10 in 150 B Use 3 14 for pi LITE

S4 Segments that Meet Outside the Circle Solve for x Assume that lines which appear tangent are tangent X X 9 15 1 of 10

T t B C TT T Tt Using the diagram what is the percent chance that the offspring are homozygous dominant for the trait A 25 50 75 t Tt tt

A n double napped hyperbola O circle parabola ellipse is a conic section formed when a plane intersects both nappes of a cone

Five years after 650 high school seniors graduated 400 had a college degree and 310 were married Half of the students with a college degree were married What is the probability that a student does not have a college degree or is married A 31 65 B 56 65 O 5 13 9 13

Use the information and table to answer the following question The table shows the results of a random survey of students in Grade 9 and Grade 10 Every student surveyed gave a response Each student was asked if he or she exercised less than 5 hours last week or 5 or more hours last week Grade 9 Students Grade 10 Students A For this question choose TWO answers Based on the results of the survey which of the following statements are TRUE B C Less Than 5 Hours 5 or More Hours 63 51 D 49 58 More 10th grade students were surveyed than 9th grade students More than 50 of the students surveyed exercised less than 5 hours last week Less than 50 of the 10th grade students surveyed exercised 5 or more hours last week A total of 221 students were surveyed E A total of 107 9th grade students were surveyed

Events M and N have probabilities such that P M 0 4 P N 0 28 P M U N 0 56 and P Mn N 0 12 Are event M and event N independent A Yes because P M P N P M U N B No because P M P N P Mn N C Yes because P M P N P M U N D No because P M P N P Mn N

8 The two way table shows the classification of studenin a mathematics class by gender and dominant hand A student who is ambidextrous uses both hands equally well Male Female Total A 12 30 B D What is the probability that a randomly selected student in the class is female given that the student is right handed 12 23 C 23 30 Right handed 11 12 23 1 Left handed 4 2 6 Ambidextrous 1 0 1 Total 16 14 30

Use the Venn Diagram to complete the following sentence Club Membership Chess Club There are 5 Select One 2 8 Science Club Select One 3 4 Math Club 3 2 students in both the math club and the science club but not the chess club Save

Given set P 5 1 3 and set Q 4 2 1 2 3 What is Pn Q A 1 2 3 B 5 4 2 1 2 3 C 1 3 D do not have an intersection

Use the graph of y f x to graph the function g x f x 3 4 y f x Ay 16 A Show Transcribed Text G Choose the correct graph of g below OA U OB oo

Eliminate the parameter t Then use the rectangular equation to sketch the plane curve represented by the given parametric equations Use arrows to show the orientation of the curve corresponding to increasing values of t x 2 3 cost y 1 2 sint 0sts Choose the correct equation and then select the correct choice for the restrictions below filling in the answer box es to complete your choice if necessary Simplify your answers The rectangular equation is A x B A C x OD There are no restrictions on the values of x and y Choose the correct graph below b F yz x sys 3 AY with restrictions Q O B 6 3 Ay 3 Q G Q O C H 3 Ay H H Q Q O D W of To X

Which point is on the circle centered at the origin with a radius of 5 units Distance formula x x V V O 2 21 O 2 23 O 2 1 O 2 3

4 What is the 3D figure that is produced when the triangle below is continuously rotated a h m What is the height of the 3D figure formed What is the diameter 3

Which equation represents a circle that contains the point 2 8 and has a center at 4 0 Distance formula x x V V1 O x 4 y 100 O x 4 y 10 O x y 4 10 O x y 4 100

U Which equation represents a circle with the same radius as the circle shown but with a center at 1 1 O x 1 y 1 16 O x 1 y 1 4 O x 1 y 1 4 O x 1 y 1 16

Which equation represents a circle with a center at 4 9 and a diameter of 10 units O x 9 2 y 4 25 O x 4 y 9 25 O x 9 2 y 4 100 O x 4 y 9 100

In the diagram a circle centered at the origin a right triangle and the Pythagorean theorem are used to derive the equation of a circle x y2 2 Q 0 0 X A P x y E S If the center of the circle were moved from the origin to the point h k and point P at x y remains on the edge of the circle which could represent the equation of the new circle O h x k y P O x h y k 1 k x h y O x k y h 7

What is the center of a circle represented by the equation x 9 2 y 6 2 10 O 9 6 O 6 9 O 6 9 O 9 6

102 DE GN 0 0 N 3 0 5 stance formula x x V V Does the point 2 6 lie on the circle shown Explain O Yes the distance from 3 0 to 0 0 is 3 units O Yes the distance from 0 0 to 2 6 is 3 units O No the distance from 3 0 to 2 6 is not 3 units O No the distance from 0 0 to 2 6 is not 3 units

9 reflection across y 3 Ay K L X

6 Which object is formed when right triangleKST is rotated around leg RS a A pyramid with a square base b An isosceles triangle c A right triangle ng R d A cone S

What is the radius of a circle whose equation is x y 8x 6y 21 0 2 units 3 units 4 units 5 units

1 What is the 3D figure that is produced when the triangle below is continuously rotated around m a A cone with radius 14 b A cylinder with radius 16 c A cone with radius 16 d A cylinder with radius 14 Test 16 3

Which equation represents a circle with a center at 3 5 and a radius of 6 units O x 3 5 6 O x 3 5 36 O x 3 y 5 6 O x 3 2 y 5 36

5 If an equilateral triangle is continuously rotated around one of its medians which 3 dimensional object is generated a Cone b Pyramid C Prism d Sphere

3 The semi circle below is continuously rotated around the 12 cm diameter listed below What is the 3D figure produced 12 cm

they related 6 How would you describe the difference between 2D figures and 3D figures How are

6 translation x y x y 5 y D A C E X

2 What is the 3D figure that is produced when the triangle below is continuously rotated around m 4 What is the height What is the radius I Im jeberi via

5 An isosceles right triangle whose legs measure is continuously rotated about one of its legs to form a three dimensional object The three dimensional object is a a Cylinder with a diameter of 6 b Cylinder with a diameter of 12 Cone with a diameter of 6 C d Cone with a diameter of 12

The local pizza restaurant offers free delivery if you live within a 6 mile radius of the restaurant The restaurant is located at the origin Ada s house is 4 miles west and 5 miles north of the restaurant at point 4 5 Does Ada s house lie on or within the circle representing the area that gets free delivery O No the distance from the restaurant to Ada s house is 41 miles which is greater than the 6 mile maximum radius O Yes the distance from the restaurant to Ada s house is exactly 6 miles O No the distance from the restaurant to Ada s house is 7 miles which is greater than the 6 mile maximum radius O Yes the distance from the restaurant to Ada s house is 20 miles which is less than the needed 6 mile radius A

10 reflection across x 1 Ay H X

3 Using a pair of scissors Rose cuts the circle out from the piece of paper a If she rotates the circle around the diameter what 3D figure is formed b Draw the 3D figure below O

4 The square above is continuously rotated around line m a Draw the 3D figure below that is produced by the continuous rotation b What 3D figure is produced What is the height and radius of the figure 2 J 1 121

A circle centered at 1 2 has a diameter of 10 units Amit wants to determine whether 2 2 is also on the circle His work is shown below The radius is 5 units Find the distance from the center to 2 2 4 The point 2 2 doesn t lie on the circle because the calculated distance should be the same as the radius F Is Amit s work correct O No he should have used the origin as the center of the circle O No the radius is 10 units not 5 units O No he did not calculate the distance correctly O Yes the distance from the center to 2 2 is not the same as the radius

5 translation x y x 5 y 1 y G F H

5 4XYZ and AXYZ are similar triangle Find the value of d Y R X 50 50 S 98 98 30 40 32 d 32 32 T Z

3 Gabe takes his license out of his wallet If he was to rotate his license around the longer edge what figure is theoretically formed a Cone b Cylinder c Prism Ruramid

YOU DO ROUND 1 1 The triangle above is continuously rotated around the leg that measures 6 a Draw a picture that represents the 3D figure produced b Name the 3D figure c What is the height of the figure d What is the radius and diameter of the figure 6 8