2D Geometry Questions and Answers

AVXZ is equilateral and ZY ZW Complete the proof that XY WX Z 1 2 3 4 5 6 Y X ZY ZW Statement AVXZ is equilateral W LYXZ ZVXW XZ VX AXYZ AXWV XY WX V Reason Given Given Vertical Angle Theorem Additive Property of Angle Measure Additive Property of Length All right angles are congruent Angles forming a linear pair sum to 180 Definition of angle bisector Definition of equilateral triangle

What single transformation was applied to quadrilateral A to get quadrilateral B B Choose 1 answer 00 A Translation Rotation

4 Priya is teaching her younger cousin to ride a bike She wants to stay on roads that are not too steep and easy enough for a new bike rider She has decided the roads must have an angle less than or equal to 7 degrees A 7 degree angle in a right triangle has a 3 25 ratio for the legs List the legs of 2 right triangles that would be safe for a new bike rider

1 point Determine if triangle FGH and triangle IJK are or are not similar and if they are state how you know Note that figures are NOT necessarily drawn to scale H A 53 F G K 53 81 Similar SSS three sides proportional Similar SSS three sides congruent Similar SAS two proportional sides and included angle congruent Similar AA two angles congruent Not Similar the sides given are not proportional Not Similar there is only one pair of congruent angles

Consider the function f x 2x 3x 36x 54 a Find the first derivative f x b List any critical values c Identify intervals of increase d Identify intervals of decrease e Find the second derivaitve f x f Use parts b through e to identify maximums as points g Use parts b through e to identify minimumns as points h Use the second derivative to identify intervals where f z is concave up i Use the second derivative to identify intervals where f x is concave down j Use the second derivative to find any inflection points k Upload a sketch of the function based on the information above and the intercepts Choose File No file chosen

Consider a system of two nonlinear first order ODEs where r and y are functions of the independent variable t 2tanh r 2r cos y 1 3cosh z 3e y sin x a Write down in matrix form of the type X AX with X x y the system obtained by linearisation of the above equations around the point z y 0 Specify the elements of the matrix A b Find the eigenvalues and eigenvectors of the matrix A obtained in a Write down the general solution of the linear system e What type of fixed point is the equilibrium solution r y 0 Sketch the phase portrait of the linear system d Find the solution of the linear system corresponding to the initial conditions z 0 1 y 0 0 Determine the values lim r t and lim y t

following crosstabulation regarding their educational level and their monthly salary 1000 2999 ILS 55 15 The variable educational level has the Tawjihi Community College University Total Select one a ordinal scale of measurement O b interval scale of measurement O c ratio scale of measurement 3000 4999 ILS 35 95 20 150 5000 7999 ILS 10 25 50 Tot 10 14 60 30

Find the value of x for which m n m 3x 32 2x 27

Determine the 4th coordinate of parallelogram JKLM 6 4 2 6 4 2 2 4 6 2 4 M 6

If the lengths of the sides of a triangle are a b and c and the height of the triangle is longer than side c which describes the triangle a C h b

A dilation has center 0 0 Find the image of the point L 2 0 for the scale factor 7 L Type an ordered pair Simplify your answer www

The figure below is dilat by a factor image Click twice to plot a segment Click a segment to delete it y 10 9 8 7 6 5 4 3 2 K 10 9 100 M N 24 H 54 5 9 7 8 9 10

Savannah is flying a kite holding her hands a distance of 2 5 feet above the ground and letting all the kite s string play out She measures the angle of elevation from her hand to the kite to be 32 If the string from the kite to her hand is 75 feet long how many feet is the kite above the ground Round your answer to the nearest tenth of a foot if necessary

Consider the following diagram A B C D If the blue lines represent possible pathways how many ways are there travel from point A to point D if we must pass through point B and C an movements are only made going down and to the right

Think About a Plan A manufacturer is making cardboard boxes by cutting out four equal squares from the corners of the rectangular piece of cardboard and then folding the remaining part into a box The length of the cardboard piece is 1 in longer than its width The manufacturer can cut out either 3 x 3 in squares or 4 x 4 in squares Find the dimensions of the cardboard for which the volume of the boxes produced by both methods will be the same o How can you represent the volume of the box using one variable o What system of equations can you write o Which method can you use to solve the system

Solve for angle B B 235 m 275 m

The graph of the increasing function f is shown in the xy plane If the function is de h x f x which of the following must be true for all values of 27 Oh x 20 OK x 0 Oh x 20 Oh x 0 Ohx 0

Let f be the linear function in blue and let g be the parabolic function in red below If you are having a hard time seeing the picture clearly click on the picture It will expand to larger picture on its own pag Note If the answer does not exist enter DNE 1 fog 2 2 gof 2 3 fof 2 4 gog 2 5 f g 4 E 6 f g 2 Note You can earn partial credit on this problem 1 0 X

In the figure shown what is the value of x B X 13x12 A C F LL 7x 6 E

i x intercept ii y intercept iii Holes iv Vertical Asymptotes v Horizontal Oblique Asymptotes vi The end behaviours vii Defining Intervals viii Sketch by hand a f x 5 x 2 b f x 5 2x 5

the circle defined by x y 4x 1 0 Show Transcribed Text

Refer to the graph of y f x shown on the right Find the absolute minimum and the absolute maximum over the interval 1 13 OB The absolute minimum is at x Round to the nearest integer as needed 15 O A The absolute maximum is at x and x 7 54 and x Round to the nearest integer as needed Use ascending order 0 OB The absolute maximum is at x f x Round to the nearest integer as needed 0 Identify the absolute minimum Select the correct choice below fill in any answer boxes within your choice O A The absolute minimum is at x Round to the nearest integer as needed Use ascending order 7 14 O C There is no absolute minimum Identify the absolute maximum Select the correct choice below fill in any answer boxes within your choice Q 37

11 In rectangle RECT above mzCRE 3x and TRC 5x 10 What is the m RCE a 10 R b 30 c 50 d 60 T

II Diagonals are perpendicular III Diagonals bisect each other IV Diagonals bisect angles Which of these are all properties of a RECTANGLE a I only b II and III c I and III d IV only

10 In parallelogram JKLM above mz 6x and m M 12x What is the mZK a 10 b 60 c 120 d 170 M

15 When is a rectangle a square a When diagonals are congruent b When diagonals bisect each other c When diagonals bisect angles d When all four angles are right angles

14 In kite KITE KM x 9 and TK 3x What is the length of TK a 3 b 13 5 c 27 d 54 K M

13 In square ABCD above BA 3x 9 units and LB 15x What is the area of the square a 6 units b 36 units 81 units d 6 561 units C

8 Using the kite from 5 determine what type of triangle AMPN is a Scalene b Right scalene c Isosceles d Right

He did the work below His work is incorrect but he correctly answers a different question What transformations did Jim Jom perform Jim Jom s Work R 40 AT 40

Q2 Q3 the shape 90 CW around the origin What quadrant will the image be in What happens to the image placement as you move the center of rotation along the x axis in the positive direction 7 Given X is the midpoint of NR and AG Prove AANX AGRX N A 2y 3 Q1 04 8 Solve for x and y given that AABC AZNI Then find mZN B 5y C G Z 4x 13 3y 10 N By 11

0 A helicopter spots two landing pads in opposite directions below The angle of depression to Pad A and Pad B is 43 and 16 respectively If the straight line distance from the helicopter to Pad A is 7 miles find the distance between the landing pads Write your answer in a complete sentence for full credit Round your answer to the nearest tenth

5 Given Quadrilateral ABCD with A 5 0 B 1 4 C 3 1 and D 3 3 Prove ABCD is a rectangle but not a square

3 4 02 Review ADEF is the image of AABC after Ty 0 What are the coordinates of D A X

tices A 5 0 B 1 3 C 2 1 D 4 2 Prove Quadrilateral ABCD is a rectangle Prove Quadrilateral ABCD is not a rhombus Justify mathematically and explain A B

In kite P mzPQR 78 and mzTRS 59 What is mzPST a 78 ei able contain signs woman to avion of phil b 62 c 59 albero d 31 MAS SU Simato0 2 R T

ZJ and LM are base angles of isosceles trapezoid JKLM If m2J 18x 8 and mZM 11x 15 find m2K A 1 B 26 D 77 154

What is not a property of a Kite answer choices Diagonals are perpendicular to each other One pair of opposite angles are congruent Two pairs of consecutive sides are congruent Diagonals bisect each other

Answer choices x 4 5 X 4 Of X that makes that shape a kite 4x 1 17 6x 3 21

Find for 0 0 360 in the following csc 0 5 and cot0 0

O SEGMENTS AND ANGLES Segment addition and midpoints In the figure below B is between A and C and C is between B and D If AC 12 AD 19 and BD 11 find BC BC 0 B D X

In the figure below O is between M and P and N is the midpoint of MO If NO 8 and NP 13 find MP MP 8 P

NP Find each measure J K and L are midpoints of NO OP and PN respectively X 95 f x X X T DXI IA LP 1 J th NL 2T 31

Suppose the equation of line p is x 2 and the equation of line q is x 1 What translation is equivalent to pra To Tmn where m n and n

A contractor builds two models of homes model A and model B The model A requires 200 worker days of labor and 200 000 in capital and model B requires 700 worker days of labor and 350 000 in capital The contractor has a total of 7000 worker days and 4 20 capital available per month The profit is 60 000 on model A and 105 000 on model B Building how many of each model will maximize the monthly profit What is the maximum possible profit Building how many of each model will maximize the monthly profit Choose the correct answer below OA Profit is maximized with 0 models of A and 21 models of B with 7 models of A and 8 models of B or with 14 models of A and 4 models of B OB Profit is maximized with 0 models of A and 21 models of B with 8 models of A and 7 models of B or with 14 models of A and 4 models of B OC Profit is maximized with 0 models of A and 21 models of B with 8 models of A and 7 models of B or with 4 models of A and 14 models of B D Profit is maximized with 21 models of A and 0 models of B with 7 models of A and 8 models of B or with 14 models of A and 4 models of B

2 TRAP is an isosceles trapezoid m R 3x m T 4x 96 and m P 12y Determine the value of x and y below R

4 4 02 Review Graph AA B C after Tx 1 A 10 In A AA

In isosceles trapezoid QUAD AD 3x feet AU x 9 feet UQ 4x 72 feet and QD 8x feet a Solve for x b What property did you use to solve for x c Determine the length of DA and UQ D

3 Find m FAB B 3x 2 www 55 A

4 Find m YDC Y D 15x 5 6x 6