2D Geometry Questions and Answers

4 The square above is continuously rotated around line m a Draw the 3D figure below that is produced by the continuous rotation b What 3D figure is produced What is the height and radius of the figure 2 J 1 121

A circle centered at 1 2 has a diameter of 10 units Amit wants to determine whether 2 2 is also on the circle His work is shown below The radius is 5 units Find the distance from the center to 2 2 4 The point 2 2 doesn t lie on the circle because the calculated distance should be the same as the radius F Is Amit s work correct O No he should have used the origin as the center of the circle O No the radius is 10 units not 5 units O No he did not calculate the distance correctly O Yes the distance from the center to 2 2 is not the same as the radius

3 Gabe takes his license out of his wallet If he was to rotate his license around the longer edge what figure is theoretically formed a Cone b Cylinder c Prism Ruramid

YOU DO ROUND 1 1 The triangle above is continuously rotated around the leg that measures 6 a Draw a picture that represents the 3D figure produced b Name the 3D figure c What is the height of the figure d What is the radius and diameter of the figure 6 8

2 What 3D figure is produced rotating the triangle continuously around line m Drawing the rotation is required for full points a Cone with a height of 2 units b Cone with a height of 3 units c Cylinder with a height of 2 units d Cylinder with a height of 3 units

7 reflection across the x axis y R A S X

3 translation x y x 6 y 2 y V U T

a What is the best name for ABCD b What is the area of ABCD 2 a What is the best name for HEG b What is the area of HEG D A 00 C G

8 reflection across the y axis B D X

What is the radius of a circle given by the equation x y 2x 8y 47 radius units

2 translation x y x y 1 R T y S X

Consider a circle whose equation is x y 4x 6y 36 0 Which statements are true Check all that apply To begin converting the equation to standard form subtract 36 from both sides To complete the square for the x terms add 4 to both sides The center of the circle is at 2 3 O The center of the circle is at 4 6 O The radius of the circle is 6 units O The radius of the circle is 49 units

A circle has a diameter of 12 units and its center lies on the x axis What could be the equation of the circle Check all that apply x 12 y 12 x 6 y 36 x y 12 x y 144 x 6 y 36 x 12 2 y 144

201 18 16 14 12 10 8 6 4 2 y X 246 8 10 12 14 16 18 20 Concentric circles are circles with the same center but different radii Which equations represent concentric circles along with the circle shown in the graph Check all that apply x y 25 x 8 2 y 9 3 x 8 2 y 9 2 14 x 8 2 y 9 3 x 8 2 y 9 25 x 9 2 y 8 3

District 131 Unit 3C Formative 3 Directions Show all work to earn full credit Round answers to the nearest hundredth and include units when appropriate Diagrams are not always drawn to scale Learning Objective 3 3 1 Determine whether a particular point lies on a given circle Learning Objective 3 3 2 Translate between the geometric and algebraic representation of a circle 1 Given the circle represented by the equation x 1 y 7 16 does the point 5 3 lie on the circle Explain your thinking

There are four steps for converting the equation x2 y 12x 2y 1 0 into standard form by completing the square Complete the last step 1 Group the x terms together and the y terms together and move the constant term to the other side of the equation 2 12x y 2y 1 2 Determine b 2 2 for the x and y terms 12 2 2 36 and 2 2 2 1 3 Add the values to both sides of the equation 2 12x 36 y 2y 1 1 36 1 4 Write each trinomial as a binomial squared and simplify the right side x P y 7

9x b E Fredy says the angle relationship is vertical and the equation should be 9x 6 8x 14 8x 14 C Brick says the angle relationship is vertical and the equation should be 9x 6 14x 10 8x 14 360 Sue says the angle relationship is supplementary and the equation should be 9x 6 14x 10 10 180 Who do you agree with Explain your thinking then solve the correct equation and solve for x then find the measure of each angle

Two LORAN radio stations A and B are 130 kilometers apart and send a simultaneous radio signal to a ship B P The signal from B arrives 0 0001 seconds before the signal from A If the signal travels 300 000 kilometers per second find the equation of the hyperbola on which the ship is positioned Use a coordinate system where the origin is the midpoint between the stations and the stations lie on the x axis

7 You are building a rectangular pen in your back yard for your dog One side of the pen will be bounded by your house The pen is to have an area of 325 square meters Determine the dimensions of the pen that will minimize the amount of fencing needed to build the remaining three sides Draw this scenario

Triangle 1 has an angle that measures 18 degrees and an angle that measures 96 degrees Triangle 2 has an angle that measures 18 degrees and an angle that measures x degrees where x 96 degrees Based on the information Terry claims that Triangle 1 cannot be similar to Triangle 2 What value of x will refute Terry s claims

Given information about the graph of a hyperbola find its equation vertices at 2 2 and 14 2 and one focus at 15 2

We let P be any point on line 7 but different from point X X

at the vertices of the triangle Find the shaded area golf tee in terms of a b Find the area of the shaded region in the figure below each square in the grid is 1 unit by I unit

Exercise 5 Find the six sixth roots of 1296 cos in standard form rounding to the nearest tenth as needed sin sin Write your answer

A pilot flies in a straight path for 1 h 30 min She then makes a course correction heading 10 degrees to the right of her original course and flies 2 h in the new direction If she maintains a constant speed of 650 mi h how far is she from her starting position Your answer is Enter your answer rounded to two decimal places mi

A Ferris wheel with a diameter of 164 feet was built in a city The top of the wheel stands 168 feet above the ground Use the diagram in the figure below as a mode wheel Round your answers to the nearest whole number a Find hifis 150 00 h 158 x b Find h if 0 is 240 0 hw c Find h if 9 is 315 0 M P A

2 The graph of trapezoid WXYZ is shown Graph the image of WXYZ after a reflection across the y axis Write the coordinates of the reflected image Example 1 N YA W 10 XV X

20 The following information on age and number of hours exercised was gathered about 13 members at a small gym 25 36 44 5 4 57 Age Hours 6 a Create a scatter plot 3 marks 22 6 5 2 D 25 43 5 4 19 33 40 44 28 25 2 5 6 5 7 4 5 3 5 5 b Determine the correlation coefficient 2 marks c Describe the type of relation and the strength of the relation 2 marks d Does the age of a gym member affect the number of hours that he or she exercises per week 2 marks How reliable and valid do you think the information is 2 marks

What is the exact value of tan 30 Enter your answer as a fraction in simplest form by filling in the boxes

What is the value of 0 for the acute angle in a right triangle sin 0 cos 48 Enter your answer in the box

What is the value of x 04 O 4 3 08 0 8 3 60

14 Find mDF a 72 b 82 c 92 d 102 C 170 F 5 44

13 If mVYX 280 and m UVX 3x 5 find the value of x W D a 9 b 11 c 15 d 18 15 Find m PQR a 29 b 39 c 49 d 59 P Q 121 S R

12 Find m NSR a 63 b 68 c 113 d 118 N 186 S 50 R

Circle P has its center at 3 1 and a radius of 4 Circle Q has its center at 7 6 and a radius of 8 Which series of transformations of circle P shows that the two circles are si a translation 4 units right and 5 units up then a dilation with scale factor 4 centered at 3 1 a translation 4 units right and 5 units up then a dilation with scale factor 2 centered at 7 6 a translation 4 units right and 5 units up then a dilation with scale factor 4 centered at 7 6 a translation 4 units right and 5 units up then a dilation with scale factor 2 centered at 3 1 A B C D

Find the scale factor and ratio of perimeters for a pair of similar trapezoids with areas 81 cm and 64 cm The scale factor is Simplify your answer

In the figure below AMNO APOR Determine the length of QF M P 10 4x 2 A N 2y 3 21 3 12 x y R

Mark did a survey to determine what the favorite food in his school was He asked 50 students in his school what their favorite food was The results are shown in the table below Boys Girls Hamburgers Pizza Tacos Hot Dogs A B 96 8 4 6 If Mark randomly selects a boy what is the probability that the boy s favorite food is tacos ESTA 12 1 10 8 5

The pair of figures to the right are similar Compare the first figure to the second Give the ratio of the perimeters and the ratio of the areas The ratio of the perimeters is Simplify your answer 10 in 14 in

A person wants to estimate the number of fish that are in a lake Which of the following would be least useful in determining the number of fish in a lake the average number of fish per square mile A B D the length and width of the lake the depth of the lake the number of fish caught per day

Triangle KNM is shown What is true about the sides of KNM K 25 A N 130 KN NM KN NM KM KM 2 NM 25 KN KM M

4 19 X 6 triangle Nienste a 25 A 3 Lo thanghe Hiaste

Chang knows one side of a triangle is 13 cm Which set of two sides is possible for the lengths of the other two sides of this triangles A D B C 5 cm and 8 cm 6 cm and 7 cm 7 cm and 2 cm 8 cm and 9 cm

10 9 8 7 6 5 4 3 2 1 A B D This graph shows triangle EFG C E FNPTY PRO 9 6 7 9 10 10 8 546265 The transformation x y x y maps triangle EFG to triangle E F G Felect the true statement N 3456 The coordinate of F is 8 1 The coordinate of E is 4 4 8 9 10 The coordinate of G is 2 3 The coordinate of F is 1 8

The probability that Milo will be assigned math homework is 0 35 The probability that he will be assigned both math and writing homework is 0 20 The probability that he will be assigned either math or writing homework is 0 65 What is the probability that Milo will be assigned writing homework B C D 0 10 0 15 0 30 0 50

The fair spinner shown below is used in a board game 2 In the game a player spins the spinner twice and finds the sum of the results of both spins The player then moves forward that many spaces on the game boa How many different numbers of spaces are possible for the player to move forward Enter your answer in the box

Look at the three dimensional solid below Which two dimensional shape can be rotated to create this solid D B C A 4 A

The coordinate plane below shows point P 2 2 and the line y x 1 ON P 2 2 B C 6 5 4 3 2 10 23456X 321 2345 2 54 3 5 6 Which equation describes the line that passes through point P and is perpendicular to the line on the graph A y x 3 y x 1 y x y x 3 D y x 1

C D Ricardo has a square hot tub He wants to build a square pool next to it that is a dilation of the hot tub using a scale factor of 5 If the pool is to be 24 ft on each side what is the length of one side of the hot tub A B DC A B D 4 ft 4 8 ft 6 ft 7 2 ft B 24 ft C

Which rule explains why these triangles are congruent X A B AAS SAS H W Y V