2D Geometry Questions and Answers

125 0 V X W In the diagram of circle C mZVWX is 43 What is m 39 41 78 82

Segments RT and SU are diameters of circle O R 94 O What is mSRT 258 266 O274 282

76 A 0 C What is the measure of ZC 38 O 76 90 O 152

Two circles are concentric if they have the same center 10 9 8 7 to LE 3 1 y 1 2 3 4 5 6 18 9 10 Which equation represents a circle that is concentric with the circle shown but has a radius that is twice as large O x 4 y 6 4 O x 4 y 6 16 O x 6 2 y 4 16 x 6 2 y 4 4

The face of a clock is divided into 12 equal parts The radius of the clock face is 10 inches Assume the hands of the clock will form a central angle no 98 11 12 7 6 1 5 2 m A Which statements about the clock are accurate Select three options The central angle formed when one hand points at 1 and the other hand points at 3 is 30 O The circumference of the clock is approximately 62 8 inches The minor arc measure when one hand points at 12 and the other hand points at 4 is 120 The length of the major arc between 3 and 10 is approximately 31 4 inches The length of the minor arc between 6 and 7 is approximately 5 2 inches

Circle O has a circumference of approximately 28 3 cm T What is the approximate length of the radius r O 4 5 cm O 9 0 cm O 14 2 cm O 28 3 cm

Triangle JKL is equilateral One side of the triangle JL is a diameter of circle M Which is true about line segments JK and KL O Both segments are tangent to circle M but are not chords O One segment is tangent to circle M and one segment is a chord in circle M O Both segments are chords in circle M but are not tangents ONeither segment is a chord nor tangent to circle M

Line segment ON is perpendicular to line segment ML and PN 10 M 25 N U 10 What is the area of triangle MOL O 200 square units O 250 square units O 300 square units O 500 square units

Line EF is tangent to circle at point A B E G A D If the measure of ZCAE is 95 what is the measure of CBA O 90 O 95 O 190 O 195

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