Geometry Questions

4 Let k be a real number such that 1 k 0 Draw a figure that represents the value of sin x sin k Your figure should NOT involve the graph of y s

Find the length of a rectangular lot with a perimeter of 94 m if the length is 5 m more than the width O O O OA 26 m B 21 m OC 47 m OD 52 m

For what values of x and y are the triangles to the right congruent by HL X A x 1 Ay y 11

A Prove AD FD D E ZAEF AAEF is isosceles F Statement Reason

Classify the graph of the equation as a circle a parabola an ellipse or a hyperbola x2 9x 2y 69 0 O circle O parabola O ellipse O hyperbola

A Given ED bisects ZAEF AAEF is isosceles Prove AD FD D E F Statement Reason

A ven AB DC AAED is isosceles Prove AABE ADCE E B C D Statement Reason

5 Given ZM 20 NP bisects MO Prove AMNP AONP N Statement Reason

Find the standard form of the equation of the circle with the given characteristics Center 1 6 point on circle 4 1

Write the equation of the circle in standard form Then identify its center and radius 9x 9y2 126x 72y 416 0 Center Radius

Find the standard form of the equation of the parabola with the given graph 2 4 6 5 4 3 9 y 7 5 3 2 1 1 3 5 7 0 0 1 2 X

Find the standard form of the equation of the parabola with the given characteristic s and vertex at the origin 1 1 1 0 Focus

Allocation of overhead Supervision expenses Materials Personnel Manufacturing Packaging Totals Utilities Materials Personnel Manufacturing Packaging Totals Insurance Materials Personnel Manufacturing Packaging Totals Allocation Base Number of employees Number of employees Number of employees Number of employees Allocation Base Square feet occupied Square feet occupied Square feet occupied Square feet occupied Allocation Base Asset values Asset values Asset values Asset values of allocation base Numerator 28 7 63 42 140 Cost to be Denominator of Total allocated 39000 6500 65000 19500 130000 140 140 140 140 of allocation base Cost to be Numerator Denominator of Total allocated 130000 130000 130000 130000 12 600 00 63 000 00 3 150 00 63 000 00 31 500 00 63 000 00 15 750 00 63 000 00 63 000 00 Allocated 20 82 800 00 16 560 00 5 82 800 00 4 140 00 45 82 800 00 37 260 00 30 82 800 00 24 840 00 82 800 00 of allocation base Cost to be Numerator Denominator of Total allocated cost Allocated cost 30 53 000 00 15 900 00 5 53 000 00 2 650 00 50 53 000 00 26 500 00 15 53 000 00 7 950 00 53 000 00 Allocated cost 20 24 000 00 4 800 00 5 24 000 00 1 200 00 50 24 000 00 12 000 00 25 24 000 00 6 000 00 24 000 00

Find the values of x and y X 72 yo 520

Points S and I are midpoints of the sides of triangle FGH 4 cm G O S What is GF 16 cm 4 cm 6 cm 8 cm H 6 cm 8 cm F

Suppose you are given set A of n points in the Cartesian coordinate system as follows A P P Each point in p points in t A has x a coordinate and a y coordinate However the y coordinate of all t 1 set A is the same For example p x y p x2 y p 3 y etc x3 Now you need to design an algorithm to determine the two losest points The running time of your algorithm should be Ofalogn a Briefly explain your strategy in solving this problem in Oinlogn running time You can draw a diagram ifneeded b Then develop your algorithm and write it in the pseudocode format similar to the algorithms discussed in the class Clearly er bound of your algorithm is O nlogn

Graph the hyperbola Give the domain range center vertices foci and equations of the asy 64x 81y 5184 81 OC y 64 9 OD y gXx The hyperbola 64x 81y 5184 has foci at 145 0 145 0 Simplify your answer Type an exact answer using radicals as needed Use a comma to separate answers as needed Type an ordered pair using integers or fractions Graph the hyperbola Choose the correct graph below OA OB O C O D

Graph the hyperbola x y 9 Give the domain range center vertices foci and equations of the asymptotes for the figure The hyperbola has a center at 0 0 Type an ordered pair AUCKEND The vertices are 3 0 3 0 Type ordered pairs Use a comma to separate answers as needed The foci are 3 2 0 3 2 0 Type ordered pairs Type an exact answer using radicals as needed Use a comma to separate answers as needed What are the equations of the asymptotes Choose the correct answer below A y 3x B x y C x 3y D y x Graph the hyperbola x y 9 Choose the correct graph below OA O C 4 OB O D Q

Write a coordinate rule for the composition the blue preimage to the green image 6 T D 2 y FV E X

Graph the ellipse Identify the center vertices endpoints of the minor axis and foci 20x 560 7y The center is 0 0 Simplify your answer Type an ordered pair The vertices are 0 4 5 0 4 5 Simplify your answer Type an ordered pair Type exact answers for each coordinate using radicals as needed Use a comma to separate answers as need The endpoints of the minor axis are 2 7 0 2 7 0 Simplify your answer Type an ordered pair Type exact answers for each coordinate using radicals as needed Use a comma to separate answers as neec The foci are Simplify your answer Type an ordered pair Type exact answers for each coordinate using radicals as needed Use a comma to separate answers as neec

Find the parametrization for the line segment joining the points P 0 1 9 and Q 0 1 9 Draw coordinate axes and sketch the segment indicating the direction of increasing t for th parametrization COB Find the parametrization for the line segment joining the two points Use P 0 1 9 as the base point and PQ as the vector Let y 1 2t X y z 0sts Type expressions using t as the variable

O are points on the circumference of O is the centre of the circle Find the rom the figure given below B C 6112 D me a b 15 35 c 50 d 65 130 e

9x y 225 The center of the ellipse is 0 0 Type an ordered pair vertices endpoints of the minor axis and foci The vertices of the ellipse are 0 15 0 15 Use a comma to separate answers as needed Type an ordered pair using integers or fractions The endpoints of the minor axis are 5 0 5 0 Use a comma to separate answers as needed Type an ordered pair using integers or fractions The foci of the ellipse are Simplify your answer Use a comma to separate answers as needed Type an ordered pair Type exact answers for each coordinate using radicals as needed

Find an equation for the line with the given properties Express your answer using either the general form or the slope intercept form of the equation of a line 1 Slope containing the point 3 3 The equation is

Graph the hyperbola x y 9 Give the domain range center vertices foci and equations of the asymptotes for the figure The hyperbola has a center at 0 0 Type an ordered pair The vertices are Type ordered pairs Use a comma to separate answers as needed

What is the Axis of Symmetry of the following parabola y x 8x 20 Ox 4 X 4 Ox 8 x 8

Find the point P at which the line intersects the plane x 8 7t y 4 7t z 7 10t 5x 4y 2z 13 The point P at which the line intersects the plane is 0 Simplify your answer Type an ordered triple

Which equation of a parabola would pass through all of the points on the graph 54 3 2 1 31 1 3 21 3 4 5 2 3 4 5 y 3 x 3 5 y 0 1 x 3 5 y 0 1 x 3 5 Oy 3 x 3 5

A line passes through the points P 8 7 3 and Q 10 6 4 Find the standard parametric equations for the line written using the base point P 8 7 3 and the components of the vector PQ y z

A lithotripter is based on an ellipse with the equation given on the right Find the distance from the ellipse s center to the kidney stone and to the beam source Use the fact that c a b The distance is Give an exact answer Simplify radicals if possible Lithotripter a machine used to crush kidney stones using shock waves The patient is placed in an elliptical tub with the kidney stone at a focus of the ellipse A beam is projected from the other focus to the tub so that it reflects to hit the kidney stone x y Equation 64 25 A 1

Find the plane determined by the intersecting lines L1 x 1 3t y 2 3t L2 x 1 4s y 1 2s z 1 2t Z 2 2s Using a coefficient of 1 for x the equation of the plane is Type an equation

Select the transformation of the graph of the parent cubic function that result in the graph of g x 3 x 2 1 Select three that apply A Horizontal stretch by a factor of 3 B Horizontal compression by a factor of C Vertical stretch by a factor of 3 D Translation 1 unit up E Translation 2 units left F Translation 2 units right

Graph the following ellipse Give the domain range center vertices endpoints of the minor axis and foci 9x y 225 The center of the ellipse is 0 0 Type an ordered pair ww The vertices of the ellipse are Use a comma to separate answers as needed Type an ordered pair using integers or fractions

Graph the ellipse Identify the center vertices endpoints of the minor axis and foci 36 y 1 The center is 0 0 Simplify your answer Type an ordered pair www The vertices are Simplify your answer Type an ordered pair Type exact answers for each coordinate using radicals as needed Use a comma to separate answers as r

A water main is to be constructed with a 25 grade in the north direction and a 10 grade in the east direction Determine the angle 8 required in the water main for the tum from north to east 0 radians Type your answer in radians Round to the nearest hundredth as needed JELEN Points 0 of 2 North East not drawn to scale

g x Identify the transformations of the graph of f x x that produce the graph of the given functio Then graph on the same coordinate plane as the graph of g x by applying the transformations to the reference points 1 1 0 0 and 1 1 g x x 3 Reference Points 1 1 0 0 1 1 First Transformation Second Transformation 4 2 4 2 0 2 4 2 4

Graph the following ellipse Give the domain range center vertices endpoints of the minor axis and foci 9x y 324 The center of the ellipse is Type an ordered pair

Write an equation for the ellipse with x intercepts 7 0 and y intercepts 0 6 D An equation for the ellipse is Simplify your answer Use integers or fractions for any numbers in the equation Type your answer in standard form

9 This design began from the construction of a regular hexagon Describe a rigid motion that will take the figure onto itself F A G B C

Find the missing values by solving the parallelogram shown in the figure The lengths of the diagonals are given by c and d Round your answers to two decimal place b 27 C 54 d 40 O L G

find the missing angle with a question mark 30 40 50 20

3 1289 X y

10 cm Find the area 18 cm 17 cm 21 cm A cm A b h

5 N X y Z W 64 yo x q wo

In 1 8 Find the value of all variables 1 110 X y 2 10 x y

6 133 X y Z to Z 20

3x 5 2x 8x 20

3y 18 9x 54 y 12

4 x y Z to 55

9 X 2x 2X 6