2D Geometry Questions and Answers

Question 3 Points 1 Which of the following is true about the scale factor of dilation O It is the ratio of corresponding angles It is the ratio of corresponding side lengths O It is the product of corresponding angles OIt is the product of corresponding side lengths

Find the translation rule and the scale factor of the dilation by transforming the circle R to R 101Y 10 R 19 6 4 2 20 2 4 R 10 2 6 X 10 Translation x y x 7 y 8 Scale factor 3 Translation x y x 7 y 8 Scale factor 4 Translation x y x 7 y 8 Scale factor 3 Translation x y x 7 y 8 Scale factor 4

Question 1 15 Points 3 Find the transformation transforming the circle C to C 10 5 20 15 10 5 0 C 5 y rule and scale factor in C2 5 10 X 15 O Translation x y x 5 y 16 and scale factor O Translation x y x 5 y 16 and scale factor Translation x y x 5 y 16 and scale factor

Which of the following statement is true O The value of it is same for all circles O The value of it is different for similar circles O The value of is same for all congruent circles O The value of is a negative number

A farmer wants to put up fencing around his rectangular field to keep his cows from grazing the growing plants 1 If the length of the field is 300 ft and the width is half of the length find the perimeter of the field Field Perimeter ft 2 If each fence consists of 5 individual strands of wire attached to a post positioned every 10 feet A How many fence posts are needed B How many feet of wire is needed posts ft of wire

5 Rewrite the following statement as a conditional statement Rick s electricity was turned off because he forgot to send in his payment O If the electricity gets turned off then Rick forgot to send in his payment O If Rick forgot to send in his payment then his electricity is turned off O If Rick s electricity is not turned off then he didn t forget to send in the payment O If Rick didn t forget to send in the payment then his electricity didn t get turned off

4 Determine if the following statement is valid or invalid You live in California if and only if you are an American O Valid O Invalid

First we wish to find polar coordinates with r 0 To find the positive value of r we choose the positive square root to solve for r SE 50 5 2 We are also asked to find such that 0 8 2 As 5 5 is in the fourth quadrant we choose a value of 0 in the fourth quadrant with 0 0 2 such that tan 0 1 7 4 7 8 To finish we find that polar coordinates of the given point with the required conditions are as follows 77 7T 5 2 4 4 r 8 50 r 5 Step 3 We are asked to find a second pair of polar coordinates for the Cartesian coordinates 5 5 We have found the following 2 50 We must now find polar coordinates with r 0 To find the negative value of r we choose the negative square root to solve for r

22 Given Prove DG DE DH DF LDGH LE Statements 1 2 LD LD 3 ADGH ADEF 4 PROOF 1 2 3 4 2 E D Reasons H F

14 Given Prove D A E ADET and ABCD AABE ACTB B Statements 1 ADET and ABCD 2 AB DT 3 LEBA LT 4 ED CB 5 LE LCBT 6 AABE ACTB PROOF Reasons 1 2 Opposite sides of a are 3 4 5 6

Classify as true or false a Any two rectangles are similar b If an angle of one rhombus is congruent to an angle of a second rhombus then the two rhombi are similar

In Exercises 5 to 8 name the method AA SSS or SAS that is used to show that the triangles are similar 5 WU 2 TR WV 2 TS and UV RS R T SU W V

In Exercises 9 to 12 name the method that explains why ADGH ADEF DG 9 DE E G DH DF D H LL F

1 Classify as true or false a If the midpoints of two sides of a triangle are joined th triangle formed is similar to the original triangle b Any two isosceles triangles are similar

Find the enlargement ratio of the circle C with center 2 8 of radius 2 units and circle C with center 4 4 of radius 6 units when C is transformed to C 1 3 5 Reset button enabled after this assessment Questions0 10 1 Reset 3 2 4

Find the measure of angle A A 8 Xx 5 B O 30 degrees O 45 degrees O 60 degrees 7 C

The length of the side AC is 8 cm Find the measure of the side AB in the given figure co 99 4 3 cm 7 9 cm 13 4 cm 14 9 cm 32 B

Find the measure of the missing side in the triangle ABC Round your answer to the nearest whole number A 15 O17 20 18 9 66 13 B

An aircraft tracking station determines the distance from a common point to each aircraft and the angle between the aircrafts If the angle between the two aircraft is equal to 49 and the distances from the point to the two aircraft are 50 km and 72 km find the distance between the two aircraft Aircraft 1 72 km O 50 km O 52 km 54 4 km X 49 Aircraft 2 50 km Res com Que 1 4 7 10

Circle C center 0 2 and radius 6 Circle C center 0 6 and radius 2 Which of the following transformation translation dilation is performed from C to C Translation 8 units up Scale factor enlargement ratio 3 Translation 8 units right Scale factor reduction ratio 1 3 Translation 8 units left Scale factor enlargement ratio 3 O Translation 8 units down Scale factor reduction ratio 1 3

Circle A center 4 0 and radius 6 Circle B center 11 0 and radius 4 Which of the following transformation is performed from circle A to circle B O Translation 15 units right and scale factor O Translation 15 units left and scale factor O Translation 15 units right and scale factor

23 Given Find 24 Given Find DE 4 AC 20 EC BC BC AD 4 AC DB AE AE 18 C S E Exercises 21 24

1 a Does the similarity relationship have a reflexive property for triangles and polygons in general b Is there a symmetric property for the similarity of triangles and polygons c Is there a transitive property for the similarity of triangles and polygons

8 Given that rectangle ABCE is similar to rectangle MNPR and that ACDE APQR what can you conclude regarding pentagon ABCDE and pentagon MNPQR E I D C R Q P

c Al A1 13 In the drawing AHJK If HK find FG AFGK 6 KF 8 and HJ 4 14 In the drawing AHJK AFGK 6 KF 8 and FG 5 If HK find HJ F K G Exercises 13 14

A B a Exercises 15 20 17 Quadrilateral ABCD BC n HJ H 16 Quadrilateral ABCD quadrilateral HJKL If mA X m J x 50 m D x 35 and mZK 2x 45 find x J b quadrilateral HJKL If AB 5 10 and JK n 3 find n 18 Quadrilateral ABCD mZD 90 AD length of diagonal HK not shown K quadrilateral HJKL If 8 DC 6 and HL 12 find the 19 Quadrilateral ABCD quadrilateral HJKL If MZA 2x4 m H 68 and m D 3x 6 find m T

1 point FORMULA FROM CUBIC GRAPH The figure shows the graph of a cubic polynomial G The function graphed is f x Hint You may write the function as f x a r b x c z d where b c and d are integers and a is a

On the Chapter 5 Test Supplement handout write an indirect proof to show that AB AD 3 points 2 3 4

The figure shows the graph of r as a function of 8 in Cartesian coordinates Use it to sketch the corresponding polar curve 1 5 2 0 1 5 1 0 0 5 1 0 0 5 R y 1 5 1 0 0 5 0 5 1 0 1 5 0 5 21 1 0 3 2 1 3 2 0 2 2 X 1 5 1 0 0 5 1 5 1 0 0 5 0 5 1 0 1 5 0 5 26 X 15 1 0 76 F

Find all x in R that are mapped into the zero vector by the transformation x Ax for the given matrix A 1 5 6 3 A 0 1 3 2 8 6 2 OA There is only one vector which is x OB X OC X 2 5 NN 132 T 2 6 N 0 accen

Find the point on the surface z 16 x y at which the tangent plane is parallel to the plane x y z 4

3 Identify the period label your vertical scale and ALL important information then graph sec x 7

Given that AABC has mZC 88 a 12 and b 22 find the remaining side length c and angles A and B rounded to the nearest tenth Provide your answer below A 22 C 88 12 C B

11 Given that cos M in Quadrant II and sin N 17 Give exact answers for all questions Give exact answers sin M Give exact answers cos N Give exact answers tan 2N Give exact answers cos MN sin Give exact answers M 1 2 Give exact answers sin M cos N tan 2N cos M N sin M 1 1 2 sin M N 4 in Quadrant III answer the following 5

Convert the following angle to degrees minutes and seconds form 29 369 The answer is 0 Simplify your answers Round to the nearest second as needed

Find the unknown angle measure in the pair of similar triangles angle B angle M O 0 0 www angle A Simplify your answers Type an integer or a fraction 27 A N17 B 109 K 170 C

Find the measure of each marked angle 0 x x 50 0 0 180 3x Simplify your answers Type integers or fractions C 40 x 50 180 3x 0

K Use the given figure to find the measures of the numbered angles given that lines m and n are parallel The measure of angle 7 is 60 The measure of angle 9 is 9 6 7 10 2 60 4 3 5 64 8 11 12 m n

3 Use the given figure to find the measures of the numbered angles given that lines m and n are parallel The measure of angle 7 is 60 6 7 910 2 4 64 8 11 12 m n

A toy rocket is shot vertically into the air from a 72 foot tall launching pad with an initial velocity of feet per second Suppose the height of the rocket in feet t seconds after being launched can be modeled by the function where is the initial velocity of the rocket and is the initial height of the rocket How long will it take for the rocket to reach its maximum height What is the maximum height

Assume Za is opposite side a LB is opposite side b and 4y is opposite side c Solve triangle ABC if ZA a 40 8 b 12 1 km and c 17 3 km Using the Law of Cosines a km Your answer should accurate to 2 decimal places Using the Law of Cosines again cos B cos Your answer should accurate to 5 decimal places Thus Your answer should accurate to 2 decimal places cos C cos y Your answer should accurate to 5 decimal places Thus y Your answer should accurate to 2 decimal places

olve each equation x in radians and theta in degrees for all exact solutions where appropriate Round approximate answers in radians to four decimal places and approximate answers in degrees to the nearest tenth Write answers using the least possible nonnegative angle measures tan x tan x 2 5

We can use the Law of Sines to find the two missing angles Select sin B sin 22 sin C sin 0 78 51 3 14 2 sin 22 10 9 22 7 sin 22 10 9 sin 0 488 29 2 B Select 0 78 0 488 The problem with those two angles is Select Find the Missing Angles Select Since Select is the longest side it must be opposite the largest angle which must mean B is an obtuse angle with a reference angle of 51 3 sin B and C 29 2

A curve is defined by the parametric equations x t 2cos t 2 and y t 4sin t Draw this graph by using the draggable points

A 120 ft height post casts a shadow that is 150 ft long What is the angle of elevation of the sun O 30 O 38 6 O 25 O 15

Question 7 Points 2 A man walked 5 miles right and read a sign that said 20 miles north to Atlanta How far is Atlanta from the starting point O 5 miles O 20 miles 20 62 miles O 25 miles

What is the formula for cos 0 O Cos 0 Opposite Cos Hypotenuse O Cos 0 Adjacent Hypotenuse Cos 0 Adjacent Opposite Hypotenuse Opposite

Question 3 Points 3 The angle of elevation of the top of a hill from its foot is 30 If the height of the hill is 200 m what is the distance of the center of the hill from its foot O 346 62 m O 116 47 m O 11 47 m 15 47 m

Question 4 Points 3 The length of a rectangular painting is 7 inches longer than its width If the diagonal is 13 inches what are the dimensions of the painting O 5 inches by 11 inches O 5 inches by 12 inches O 5 inches by 13 inches O 11 inches by 12 inches

Question 5 The angle of elevation of a car on a road to the top of a tower is 45 If the distance between the car and the tower along the road is 22 ft find the height of the tower O22 ft O 45 ft Points 1 O 67 ft O 180 ft