Geometry Questions

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

10 8 6 4 2 8 N 4 6 8 10 y 2 4 6 8 10 X A circle centered at the origin contains the point 0 9 Does 8 17 also lie on the circle Explain O No the distance from the center to the point 8 17 is not the same as the radius O No the radius of 10 units is different from the distance from the center to the point 8 17 O Yes the distance from the origin to the point 8 17 is 9 units O Yes the distance from the point 0 9 to the point 8 17 is 9 units

To derive the standard formula of a circle a radius ris constructed as the hypotenuse of a right triangle as shown D h k E x y F x What are the lengths of the sides of the right triangle that is formed Check all that apply Oh Ok Oh k O x h O x y y h Oy k

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

Lo 3 21 2 30 y N 3 4 LA X What is the equation of the circle shown in the graph O x 3 2 y2 4 O x 3 y 2 O x y 3 4 O x y 3 2

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

The equation of a circle is x y 10 16 The radius of the circle is units The center of the circle is at

Write x y 18x 8y 5 0 in standard form 1 Group terms and move the constant to the other side of the equation 2 18x y 8y 5 2 Determine the values that need to be added to both sides of the equation 18 2 2 81 and 8 2 16 3 Add the values to both sides of the equation 4 Write each trinomial as a binomial squared and simplify the right side What is the standard form of the equation of a circle given by x y 18x 8y 5 0 v

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

Find the surface area of the regular pyramid shown to the nearest whole number The figure is not drawn to scale 12 m 1 point 6 3 O1 540 m O770 m 396 m 1718 m 11 m

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

1 Find the tree length ban 49 50 tree at so tan 6 1 free tree a 50 tan 49 5 a tan 61 a tan 49 5 tan 6 1 5 0 tan 49 5 49 5 50 dan 49 5 dan 49 5 tan 61 50 ft tree axtan6 1 16P 61 0 4marks tree

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

19 Find all the complex cube roots of 8 8 3i then plot the in the complex plane

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

Calculator What is the value of x in the triangle Enter your answer in the box Round your final answer to the nearest hundredth 18 25 cm X

Calculator A party tent is used for an outdoor event Ropes of equal length support each tent pole The angle each rope makes with the ground is 55 What is the height of each tent pole Enter your answer in the box Round only your final answer to the nearest tenth MAN 25 ft 55

What are the values of the trigonometric ratios for this triangle Drag the answers into the boxes sin 0 cos tan 0 III 0 13 12 5

What is the value of x in this triangle Enter your answer as a decimal in the box Round only your final answer to the nearest hundredth X lo 29

What is the value of x 07 07 2 14 O 14 2 45

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

10 Find the value of x a 11 2 b 12 4 c 13 2 d 14 4 q x 6 6 8 4

What is the measure of a single interior angle of a regul nonagon

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

The scale factor of the dimensions of two similar wood floors is 3 2 It costs 60 to refinish the smaller wood floor At that rate how much would it cost to refinish the larger wood floor Simplify your answer

A cylinder that has a height of 20 cm and a radius of 3 cm If you were trying to find the volume of a cone with the same dimensions what would be the correct input calculation V 20 3 A V 20 3 3 V 20 3 I 3 20 4 3 11 N

Which equation describes a circle with center 4 7 and radius 9 1 4 y 7 9 x 4 y 7 2 81 x 4 y 7 9 x 4 y 7 81 A B C D