2D Geometry Questions and Answers

Consider circle N with radius 30 cm and 0 radians N 0 30 cm L M What is the approximate length of minor arc LM Round to the nearest tenth of a centimeter O 12 4 centimeters O 15 7 centimeters O 31 4 centimeters O 36 7 centimeters

The dot product of two vectors is Select one O a a real number O b a magnitude O c an integer O d a vector

Given the information a vector has length 6 with Southeast direction it could be drawn from into the and extend

identity the conic the polar equation represents and give the position of the directrix 1 2 9 sin 0 r Identify the conic that our polar equation represents Choose the result below Ellipse Parabola O Hyperbola Is the directrix perpendicular to the polar axis or parallel to the polar axis O Perpendicular Parallel Which direction is the directrix from the pole O Above Below Right Left How far is the directrix from the pole

What is the directional angle of the vector 3 7 Select one O a 293 2 O b 336 8 O c 2 33 Od 66 8

Something is traveling 7 miles per hour South This could be represented by 7 1

All vectors Select one or more a have length O b begin at the origin C are scalar Od have direction

Determine the equation of the hyperbola satisfying the given conditions Write the answer in the form Ax2 By2 C or in the form Ay2 Bx2 C Asymptotes y 4x graph passes through 1 15 2 15y 16x 240

9x 4 12x 23 VALUE OF X INISSING ANGLET

The two circles are externally tangent Write the equation of this tangent line x 2 y 2 25 and x 9 2 y 12 2 100

Show that the two triangles are similar N M X 45 Y ZNZ 45 N and ZMYNL so AMYN AXYZ

tes Renal System Unit G description of henr Grades Assignmen MS is tangent to circle O at point M and MQ is a secant line If mMQ 150 find m QMS Y 0 S M O Submalt Anque

Show that the two triangles are similar W 85 X 45 50 Z U

Find the value of x that makes ADEF AXYZ 10 D E 8 3 x 1 F 7 5 Z 4 Y X x 1

of the lake WX MATHEMATICS You can measure the width of the lake using a surveying technique as shown in the diagram Find the wid V 104 m W WX m 6 m Z Y Not drawn to scale 8 m

COMPLETE THE SENTENCE For two figures to be similar the corresponding angles must be and the corresponding side lengths mu

Complete the table of values for the equation y 5 0 Then plot the ordered pairs X 0 11 3 2 6 Simplify your answers Type integers or fractions

Express the following as a function of a positive acute angle 4 tan 96

What is the surface area of the solid The surface area of the given solid is cm Do not round until the final answer Then round to the nearest whole number as needed T 3 cm 6 cm L 4 cm

Use a net to find the surface area of the prism 5 ft Answer 4 ft 6 ft

Find the surface area of the prism The surface area of the prism is in L 11 in 6 in 5 in

For the polyhedron use Euler s Formula to find the missing number faces edges 14 vertices 7 The number of faces is Tyne a whole number

Use Euler s Formula to find the number of vertices in the given polyhedron 8 faces 2 hexagons and 6 rectangles There are vertices in the polyhedron

3 reflection across the y axis Y 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

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

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

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

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

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

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

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

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