Geometry Questions

What is the radius of a circle whose equation is x y 8x 6y 21 0 2 units 3 units 4 units 5 units

1 What is the 3D figure that is produced when the triangle below is continuously rotated around m a A cone with radius 14 b A cylinder with radius 16 c A cone with radius 16 d A cylinder with radius 14 Test 16 3

Which equation represents a circle with a center at 3 5 and a radius of 6 units O x 3 5 6 O x 3 5 36 O x 3 y 5 6 O x 3 2 y 5 36

5 If an equilateral triangle is continuously rotated around one of its medians which 3 dimensional object is generated a Cone b Pyramid C Prism d Sphere

3 The semi circle below is continuously rotated around the 12 cm diameter listed below What is the 3D figure produced 12 cm

they related 6 How would you describe the difference between 2D figures and 3D figures How are

6 translation x y x y 5 y D A C E X

2 What is the 3D figure that is produced when the triangle below is continuously rotated around m 4 What is the height What is the radius I Im jeberi via

5 An isosceles right triangle whose legs measure is continuously rotated about one of its legs to form a three dimensional object The three dimensional object is a a Cylinder with a diameter of 6 b Cylinder with a diameter of 12 Cone with a diameter of 6 C d Cone with a diameter of 12

The local pizza restaurant offers free delivery if you live within a 6 mile radius of the restaurant The restaurant is located at the origin Ada s house is 4 miles west and 5 miles north of the restaurant at point 4 5 Does Ada s house lie on or within the circle representing the area that gets free delivery O No the distance from the restaurant to Ada s house is 41 miles which is greater than the 6 mile maximum radius O Yes the distance from the restaurant to Ada s house is exactly 6 miles O No the distance from the restaurant to Ada s house is 7 miles which is greater than the 6 mile maximum radius O Yes the distance from the restaurant to Ada s house is 20 miles which is less than the needed 6 mile radius A

10 reflection across x 1 Ay H X

3 Using a pair of scissors Rose cuts the circle out from the piece of paper a If she rotates the circle around the diameter what 3D figure is formed b Draw the 3D figure below O

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

5 translation x y x 5 y 1 y G F H

5 4XYZ and AXYZ are similar triangle Find the value of d Y R X 50 50 S 98 98 30 40 32 d 32 32 T Z

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

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