2D Geometry Questions and Answers

Find the identical expression for the following 4 Cos 0 1 1 cos 0 cos 0 Hint consider the numerator as a difference of squares sin 8 tan 8 cos 8 2 sin e 2 cos 0

Write a quadratic function in STANDARD FORM whose graph satisfies the given conditions 7 a Passes through the points 4 0 3 0 2 18 b Passes through the points 1 0 5 0 3 16

g x x x 6

3

Several different kinds of cheese are for sale The cheese comes in wedges shaped like sectors of the wedges are the same height 6 7B Mai bought a wedge with a central angle of 45 degrees and a radius 10 inches What is the area of the top surface of this wedge

The circle with center B is a dilation of the circle with center A using scale factor 2 Select all true statements a a The circumference of the circle centered at B is greater than the circumference of the circle centered A by a factor of 2 b The ratio is greater than the ratio by a factor of 2 c The value of is greater than the value of a by a factor of 2 d The angle marked a measures radians 6 12 87 e The angle marked measures radians

Solve the following system of equations by graphing y 2x 6 y x 1

1 7A The image shows a circle centered at point O Angle AOB measures 50 degrees What is the measure of angle ACB Explain how you know a 25 degrees b 40 degrees c 50 degrees d 100 degrees B 50

F 1 3 m Find the surface area of each figure 12 in 5m Q 12 in 18 cm 5 cm 12 in ANS ANS 10 m ANS

4 7B A circle has a radius of 20 centimeters and a central angle that measures 216 degrees Find the length of the arc defined by this central angle

2 7A Line BC is tangent to the circle centered at A Find the measure of angle BCA Explain or show your reasoning B 57

Minor arc KL measures 135 K L Which is the radian measure of central angle KOL O O 3 radians O 3 4 radians O radians 7 8 13 T 5 radians

5 T Consider circle T with radius 24 in and 8 6 4 24 in T T1 radians What is the length of minor arc SV O 20 in O287 in 40 in O 637 in

Arc CD is of the circumference of a circle What is the radian measure of the central angle O O O 2 radians 3 3 T 4 47 3 radians radians O 3T radians TE

Circle O has a circumference of approximately 44 in P What is the approximate length of the diameter d O 7 in O O O 14 in 22 in 44 in

Circle P has a circumference of approximately 75 inches T What is the approximate length of the radius Use 3 14 for T Round to the nearest inch O O 12 inches 24 inches 38 inches 46 inches

Circle O has a circumference of approximately 2507 ft Jud O What is the approximate length of the diameter d 40 ft 80 ft O 125 ft 250 ft

Two circles are shown in the diagram C d 1 C2 d 2r Since all circles are similar a proportion can be set up using the circumference and diameter of each circle Sub the values d 1 C and d 2r into the proportion C C d d Which shows how to correctly solve for C the circumference of any circle with radius r

An arc on a circle measures 295 The measure of the central angle in radians is within which range O 0 to radians Oto radians O to 3 T 2 3 T 2 radians to 2 radians

Factor the following polynomial twice First use a common factor with a positive coefficient and then use a common factor with a negative coefficient 4 3 2x 6x 10x 6 4 Factorization of the polynomial 2x 6x 10x using a common factor with a positive coefficient is Factorization of the polynomial 2x 6x 10x using a common factor with a negative coefficient is

Consider a regular hexagon inscribed in circle C with radius r Regular hexagons have six congruent sides and six congruent angles In the figure angle CAB measures 60 What is mZACB What is the length of segment AB What is the perimeter of the hexagon The perimeter of the hexagon is the circumference of the circle The circumference of the circle is O F 1 A B

2 The equation of circle B is x 8 y 2 16 Determine the coordinates of a Center 8 2 r 16 b Center 8 2 r 4 c Center 8 2 r 16 d Center 8 2 r 4

In circle C SQ 10 cm S R C 30 P Q Which statements about the circle are correct Check all that apply O Arc PQ is congruent to arc SR The measure of arc QR is 150 The circumference of circle C is 207 cm Arc PS measures about 13 1 cm Arc QS measures about 15 7 cm

Consider circle C below where the central angle is measured in radians R C 5x 6 S 10x What is the length of the radius units

Consider circle O in which are XY measures 16 cm The length of a radius of the circle is 32 cm What is the circumference of the circle units What is the ratio of the arc length to the circumference What is the measure of central angle XOY

circle O central angle AOB measures O A 18 cm EM B radians What is the length of arc AB O 67 cm O 127 cm O 187 cm O 367 cm

Circle O has a circumference of 88 cm T What is the length of the radius of the circle cm

A VT 4 O 16 in B In circle O angle AOB measures What is the length of arc AB in I radiar 4

Arc AB is of the circumference of a circle What is the radian measure of the central angle 3 O radians O2 radians 3 O 3 radians 37 radians

Q Arl T P r O K r r J There are exactly radians in a semicircle There are exactly There are approximately 2 radians is equivalent to radians in a full circle radians in a full circle degrees

Move AA B C so it is a translation of AABC according to the rule x y x 4 y 6 10 10 A A D 5 B B 5 y 10 5 10 N

Find the length of side L in the figure shown below Perimeter 20 L 5

Quadrilateral Q U A D is a dilation of quadrilateral QU AD with a center of dilation at point P U Q U 12 07 7 1 Q What is the scale factor of this dilation 10 37 6 1 A A 7 1 12 07 D D

B C so it is a translation of AABC according to the rule x y x 4 y 4 5 Y B 51 A B x

Move AA B C so it is a transformation of AABC according to the rule x y x y 5 S y B N

Find the area of the shaded region 5 49 35 21 3 17 1 3 21 y 49 x 35 91 The total area of the shaded regi Simplify your answer

7 Draw a picture that matches this situation 8 ZREZ

If mCW 180 and m Q 58 find mSJ S W Q

What is the value of x G X X 82 X 37 X 43 E F F

Write the equation in standard form for the ellipse with vertices 0 12 and 0 12 and covertices 3 0 and 3 0

find sin2x cos2x and tan2x if sinx 4 5 and x terminates in quadrant IV

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