2D Geometry Questions and Answers

Given LV and KV are tangents of circle D find coordinate of point V L 3 6 D 9 2 K 1 4

Perform the indicated operation 3 cos 190 i sin 190 8 cos 229 i sin 229 Give your answer in polar form cos i sin

Find the area of the shaded segment Round your answer to the nearest tenth 3

7 AHGFALKJ 18 F 36 24 H 8 G S 70 55 132 E 60 R F 144

3 SAT Question The equation below defines a circle in the xy plane What are the coordinates of the center of the circle a 20 16 b 10 8 c 10 8 d 20 16 x 20x y 16y 20

4 A circle is centered at C 1 3 and has a radius of 6 Where does the point P 6 6 lie a Inside the circle b Outside the circle c On the circle d Cannot be determined

The image shows quadrilateral ABCD 1 Prove that quadrilateral ABCD is a square 2 Find the perimeter of ABCD Explain or show your reasoning 3 Find the area of ABCD Explain or show your reasoning Enter your answers and your explanation in the space provided You may also use the drawing tool to help explain or support your answer y 7 6 5 C 4 3 2 1 A 16 1 5 2 T B 3 X 8 D 4 HT 5 S 6 C 7 X

994 8 YA EX 654 327 O T F X 8 1 2 3 4 5 6 7 8 9 X The parabola in the image has its focus at 4 3 Its directrix is the line y 1 The point 8 6 is on the parabola Select all of the statements that are true Select all that apply The equation x 4 y 3 y represents the parabola The equation x 4 y 3 y 1 represents the parabola The point 8 6 is the same distacne from the point 4 3 as it is from the line y 1 The point 2 3 is on the parabola The point 0 5 5 is on the parabola If point x y is on the parabola then the distance between x y and the point 4 3 is the same distance between x y and the y axis

The triangles below are similar What is the ratio larger to smaller of the areas 15 ft 9 ft Input answer as larger smaller

1 Determine the equation of the circle below 2 5 3 A N 1 B 0 2 b

What is the area of the figure below 10 m Select one O a 72 m O b 96 m O c 36 m O d 60 m 6m 12 m

What is the area of the figure below 7 5 in Select one 6 in O a 45 in O b 90 in O c 135 in 2 O d 180 in

What is the area of the parallelogram 4 5 m 6 m 4 14 m Select one O a 84 m O b 126 m O c 63 m O d 31 5 m

What is the area of the figure below 10 8 in 10 in O b 4 in 5 in Select one O a 52 in 54 in 2 O c 27 in O d 26 in 2 3 in

Find each probability using permutations or combinations whichever is appropriate 42 A class contains 12 girls and 16 boys If a 43 To enter a video call with their teacher each student must enter a unique group of 5 people is formed from this class what is the probability that they are all boys passcode that begins with 3 capital letters that do not repeat What is the probability that a student s passcode begins with ABC 44 There are 30 calculators numbered 1 30 in a case If 4 of the calculators are broken what is the probability that the numbers on the broken calculators are at least 16 45 Laura is filling three empty photo frames on her mantle by randomly using individual pictures of her eight grandchildren If Ben i her grandson what is the probability that his picture is used in the middle frame

25 Mr Howell teaches four geometry classes On the last fest he gave 95 of the students passed the test 60 studied for the test and 48 both studied and passed the test If a student is chosen at random what is the probability that they passed the test given that they studied 26 Ryan pitched for his baseball team in 5 8th of the games it rained for 3 10th of the games and he pitched and it rained for 1 4th of the games If a game is chosen at random what is the probability that it rained given that Ryan pitched

For questions 29 34 A group of boys and girls were surveyed and asked their eye color 29 The results are shown in the partial table below Complete the table Blue Brown Green Total Boy 126 157 Girl 21 64 8 Total 49 30 Create a relative frequency table by filling in all joint and marginal relative frequencies Blue Brown Green Total Boy Girl Total

For questions 15 and 16 A point in the figure below is chosen at random Find the probability that the point lies in the shaded region Give each answer as a percent 15 16 12 cm 22 cm 10 ft 6 ft

38 The number of ways to arrange the letters in the word JOURNEY 39 The number of ways to create a 4 person committee from a group of 25 people

23 A number from 1 50 is chosen at random Find each probability as a fraction in simplest form a P odd less than 25 b P greater than 10 even 24 A letter in the grid below is chosen at random What is the probability that the letter is in the word BASKETBALL given that it landed in the shaded region ABCDE FGHIJ KLMNO PQRST

SU and VT are chords that intersect at point R S V x 6 x 1 n x 4 T What is the length of line segment VT O4 units 08 units 13 units O14 units

W 12 k 4 k N What is the length of line segment XZ O4 units 8 units 16 units 20 units

BD and AC are chords that intersect at point Y w 3 X Y 8 D S C What is the length of line segment AY O 2 units O 3 units O4 units O 6 units

Line segment BA is tangent to the circle 55 C A 120 What is the length of line segment BA Round to the nearest unit O 18 units O 65 units 88 units O 98 units

The circle is inscribed in triangle AEC A F B D C Which are congruent line segments Select two option OAB and CB OEF and ED ED and CD AF and EF CB and CD

R S T Line segment ST is congruent to which line segment OSK OKU OUT OTK

What is the definition of postulate an assumption presumed to be true that is used as the basis for a logical argument B a statement that has been shown to be true by logical argument C a statement known to be false that is used as the basis for a logical argument D a statement that has been shown to be false by logical argument A

A searchlight has a parabolic reflector that forms a bowl which is 13 in wide from rim to rim and 3 in deep If the filament of the light bulb is located at the focus how far from the vertex of the reflector is it round to at least 3 decimal places 13 3 Picture not to scale

A golfer tees off on level ground and hits the ball with an initial speed of 49 m sec at an angle of 33 above the horizontal Choose a coordinate system with the origin at the point where the ball is struck Remember to use the degree symbol if necessary Part 0 5 Part 1 of 5 a Write parametric equations that model the path of the ball as a function of time t in sec Simplify your answers as much as possible The parametric equations are X and y Osino cas

10 8 6 HERRE 4 2 8 9 6 4 2 CH 2 6 8 10 2 4 6 8 8 X 10 Q Write the standard equation for the hyperbola graphed above

se OP at the right to find the name of a minor arc whose measure is less than 82 C D 829 P 68 B 6 cm A

A factor that is necessary for the formation of a new species is OA different mating behaviors OB reproduction at different times OC geographic barriers OD reproductive isolation

What structural problem prevents adenine from pairing with guanine OA they lack the deoxyribose group OB they lack phosphate groups OC the bases are both short OD the bases are both long

The separation of populations by barriers such as rivers mountains or bodies of water is called QA genetic equilibrium B temporal isolation C behavioral isolation D geographic isolation

MatuloyDNE 7 Tameeka is in charge of designing a school pennant for spirit week What is the area of the pennant Example 3 31 1 ft 9 CLASS OF 2020 8 6 km TIGERS 6 ft Find the missing dimension of each triangle Example 4 10 b A 38 7 km2 8 Norma has an A frame cabin The back is shown below If the total area of the windows and door is 3 5 square yards how many square yards will she need to paint to cover the back of the cabin Example 3 12 642571 5 yd 6 75 in A 13 5 in h 8 yd

13 FIND THE ERROR A student is finding the height of the triangle Find the student s mistake and correct it 17h 68 h 4 meters 17 m A 68 m 15 CONSTRUCT AN ARGUMENT Mrs Giuntini s lawn is triangle shaped with a base of 25 feet and a height of 10 feet Is the area of Mrs Giuntini s lawn greater than 250 square feet Write an argument that can be used to defend your solution 14 CONSTRUCT AN ARGUMENT Determine if the following statement is always sometimes or never true Write an argument that can be used to defend your solution If a triangle and a rectangle have the same base and height the area of the triangle will always be greater 16 CREATE Draw and label a triangle with a base that is 3 times its height and has an area that is less than 50 square inches

12 B Apply the nearest neighbor algorithm to the graph above starting at vertex A Give your answer as a list of vertices starting and ending at vertex A Example ABCDA

rod connecting the piston to end of the crankshaft measures 12 cm What distance up and down in a cylinder rotates a wheel with radius 5 cm The must the piston travel to change the angle from 40 to 140 12 cm 40 Crankshaft 5 cm netry N Orlando

Given OS PR 21 22 Prove MO MT OP SR P M T Hint Use substitution property as a reason why z1 zMTO R

Given TP VW lengths Find ST TV and PT as shown 10 T W

For problems 4 6 use the figure below 3 Find the m 1

Complete the following sin 116 81 trig O Note that the given angles are in radians cos sin A op C

x 2 Spl x 4 Which equation results from applying the secant and tangent segment theorem to this figure O x x 2 x 4 O x x 4 x 2 O x x 4 x 2 Ox 2x 4 x 2

Find the area of the regular polygon 041 Round to the nearest tenth as needed Area

For problems 1 3 use the figure below Find the m1 Answer

What is the area of the regular polygon The area is m Round to one decimal place as needed

Find the area of the regular polygon with the given apothem a and side length s decagon a 22 m s 14 3 m The area is m Simplify your answer Round to one decimal place as needed

22 32 X M 14 N In the diagram the length of the external portion of the secant segment PN is The length of the entire secant segment LN is The value of x is

Examples Find the indicated angles in each of the triangles below Round your final answers to the nearest hundredth Figures may not be drawn to scale a 15 17 X X

2 If sin 0 3 0 0 a sin 20 A 0 find the exact value of each of the following 0 b cos 20 a sin 20 Type an exact answer using radicals as needed 0 c sin 2 b cos 20 Type an exact answer using radicals as needed d cos c sin Type an exact answer using radicals as needed 0 2 Type an exact answer using radicals as needed d cos