2D Geometry Questions and Answers

Given the three points A 2 6 B 4 6 and C 4 1 consider the triangle AABC and let M be the point on AC so that BM is the altitude through B perpendicular to AC Likewise let N be the point on AB so that CN is the altitude through C perpendicular to AB B i Find M ii Find N M N M diagram not to scale N Note in Maple notation the point is entered as 1 2 3 4 Challenge worth 2 points iii It is known that the three altitudes of any triangle meet at a common point called the orthocenter For AABC this orthocenter is

Solve for x 2 D A 6 C 3 B 3 E I D

of water in a wave pool oscillates feet The wave generator pumps 6 waves per minute Write a sine function that represents the height h of the water at time t seconds Then graph the function below from 0 to 30 seconds Height feet 15 14 13 12 11 10 9 8 7 5 4 3 2 AN 1 h t 5 10 15 Time seconds 20 25 30

B A 14 0 B 14 7 E D If rectangle DEFG is dilated by a scale factor of 7 with a dilation ce

If quarilateral ABCD is a square and AC 6 2 find the missing values A D AD 30 AB ED m AEB m ADC DRAG DROP THE ANSWER E 6 B 6 2 9 45 3 2

r AEFG ALMN Find LN A 3 B 2 5 c 5 D 3 5 E 7 10

15 0 The actual length L of a rectangle is 36 centimeters Use the scale drawing of the rectangle to find the actual width W A 12 54 0 3 6 cm 24 0 2 4 cm

13 The pink trapezoid has been dilated to form the blue one A 3 BLUE What factor was used to make the dilation B 4 PINK C 4

12 By which reason can it be proven that A AAS

8 A A B D 4 congruent angles C B 4 congruent sides perpendicular diagonals congruent diagonals Square Rectangle Rhombus X X X X 2 pairs of opposite sides X congruent X X X A B X X Isosce Trapez The table shown is missing an X Where should t C X D

A 2 0 B 1 5 0 5 A D 1 0 B B 32 A S 32 AABC has been dilated to AA B C Which factor was used 23 23 C

1 Statements B 1 AB AC 2 AABC is isosceles 3 BD a CD 4 ZB a C 5 AABD AACD B SAS ASA C Reasons 1 Given 2 Definition of isosceles A 3 Given 4 Base angles an isosceles triangle are a 5 227 Choose the missing reason in the proof A AAS

Q5 Find the area inside the cardioid defined by the equation r 2 2 cos 0

6 pts Let f x be the function whose graph is as follows 4 3 Y 2 1 0 0 1 2 3 4 y f x I a 4 pts Sketch the graphs of f 2x f 2x 3 f 2x 3 and f 2x 3 4 b 2 pts Extend the graph of f x to the interval 4 4 so that it is an odd functio

1 Use the given graph of f x to find 6 34 24 3 f x 13 Do NOT need to show any work A f 2 B lim f x x 2 c lim f x x 2 D lim f x T 2 E Is the function continuous at x 2 Why or why not Justify your answer 2 Use the definition of the derivative to find f of the function f x 2x 6x 5 a Write the Definition Formula of Derivative f x b Use the definition to find the derivative of the function

S 10x 41 4x 7 T 17 V U Figure 1 1 5pts Using Figure 1 above fin the dimension of segment SV SV

Question 9 As part of video game the point 1 6 is rotated counterclockwise about the origin through an angle of 30 degrees Find the new coordinates of this point X y Question Help Video

I ve the equation f x g x using the graph given 10 6 12 2 6 X Q

4 i 4 A N 14 PE N M T MS Y 7 da 9 10 What is the slope of the given line What is the slope of a perpendicular line Draw a perpendicular line that has a y intercept c Write the equations of both lines

1 Find the equation of the line passing through 2 9 and 5 21 slope intercept form Write the answer in

Find the equation of the plane that is parallel to the vectors 2 0 3 and 0 2 1 passing through the point 2 0 The equation of the plane is CEERD

Abrar is creating a model of the Pyramid of Giza using clay Abrar s model will have a square base with side lengths of 15 inches and the height of the pyramid 10 inches What will be the volume of Abrar s model

Determine whether the graph on the right is that of a function by using the vertical li a the domain and range assume that the curve approaches but never intersects th b the intercepts if any c any symmetry with respect to the x axis y axis or the ongin Does the graph represent a function Choose the correct answer below A Yes the graph is a function because every vertical line intersects the graph OB Yes the graph is a function because every vertical line intersects the graph B 2 5 4 4

Use the diagram for Items 10 13 N M e R o P 10 If m MPQ 48 find mQM 11 If mMNQ 200 then what is m MPQ 12 If mQN 125 and mQR 83 find m 1 13 If mNQR 260 and m 1 45 then what is mQN

A certain technique calls for 75 kVp 25 mAs at a SID of 175 cm The exposure at that the image receptor is 15 mGy If the SID is changed to 100 cm what will the new mAs need to be

9 Graph the function 1 point y log x 1 1

Solve the following formula for b y 3mx 46 b Enter your answer as an expression But be careful to enter an expression like both the numerator and denominator a b 3 m you need to type a b 3 m You need parentheses

Determine the measure of each indicated angle Note the figure is not drawn to scale A C 1069 21 m ACB m CBA m BAC m 1116 8 138 B

A right circular tank lying on its side has bases of radius 5 ft and a horizontal length of 12 5 ft Use the applet below to help in setting up the integral used to solve the following problem Ay X

Consider the function f x y 2 x y Plot it in GeoGebra a Draw level curves of f x y at each value 1 0 1 2 3 4 5 sy J 2 0 2 b Describe in words what the level curves look like and explain why this is t case

For the quadratic function f x x 4x answ a Graph the quadratic function by determining its vertex axis of symmetry y intercept and x i Does the graph of f open up or down

4 Find the dimensions of a rectangular parallelepiped that will maximize the enclosed volume while maintaining a constant surface area of 54 m 31 Figure 1 Parallelepiped 5 Find the interior angles of a rhombus that maximize the area with a maximum height of 12 inches and a perimeter of 64 inches Figure 2 Rhombus

Sketch the graph of f x 2x 10 yolul 10

8 Sketch the surface 1 2 5 x y Describe the boundaries of this surface

4 Find an equation describing the following sinusoidal curve y 3 4 114 5 Find an equation describing the following sinusoidal curve y t 12 7

K Use the graph to find the following a the domain off b the range of f c the x intercepts d the y intercept e intervals on which f is increasing a What is the domain of f Type your answer in Q f intervals on which f is decreasing g intervals on which f is constant h the number at which f has a relative minim i the relative minimum of f j f 6 k The values of x for which f x 3 1 Is feven odd or neither

QUESTION 2 s possible to find the area of a square by first calculating the s hat is the area of this square if the diagonal is 12 cm e the following diagram

MUTHARESE Use the graph to write a polynomial function of least degree f x 260 0 200 400 f x 400 000 200 000 200 000 100 0 200 0 67600

Function Notation Sketch the graph of y x AND y x label ea 5 Stretching and Shrinking Function Notation 10 Sketch the graph ofy x 2 AND ofy x 2 label ea y x 2 Sketch the graph of y x AND y x label e 10 Type of Transformation luvertically 104 galal Change to Coordinate Point Stretched horizontally Shrunk horizon

Use the graph to write the formula for a polynomial functio f x x 2 x 1 6 X 4 2 f x 6 4 2 4

Write the equation for the graphed function y 8 6 4 2 y 8 6 4 N 2 4 2 4

2 Find the area of the shaded region below Give your answer in square feet Note The picture is NOT drawn to scale 15 yd 300 in 150 in 18 yd 120 in 18 ft 30 ft

6 4 2 f x 6 4 2 4 6 4 6

2 Harley is building a rectangular wooden box for storage The box is going to have a base that is 2 feet long and 3 feet wide If the box needs to be able to hold 9 cubic feet of material how tall should it be in feet If the material for the box costs 0 60 per square foot how much will it cost to build the box

Clearly and neatly show all work for answers 1 Convert the following quantities Be sure to include units in your answers Round final answers to 2 decimal places where needed a 2 4 meters to centimeters b 8 cups to quarts c 12 stones to ounces d 12 pounds to grams al 22 kilomotors to vards

Highlight 2 8 Calculator ansit company operates commuter trains to help people get to the city h day Each train travels on a straight route to and from the farthest ion stopping at other stations along the route distance y miles the train is from the station after Commuter Train Distance graph shows the inutes Distance from the Station miles 322595 30 E 20 Torres Bravo 0 10 20 30 40 50 60 70 80 Time minutes Time Remaining 00 33 Question 7 a A Flag for Rea Formula Sheet Calculator Reference Type your answer in the box You may use numbers a decimal point and or a negative sign in your answer Based on the graph what was the average speed in miles per minute of the train during the interval of 30 to 40 minutes

Part 1 of 3 points Points 0 of 1 The median weight of a boy whose age is between 0 and approximated by the function w t 7 04 1 88t where t 0 0015t 2 0 000061t 3 is measured in months and wis measured in poun approximation to find the following for a boy with median w through c

2 Given AABC determine the measures of all of the sides and angles as well as the perimeter and area of the figure 12 10 00 30 e A B C 10 12

e the graph of the function f in the figure to sketch the graph of the function g Graph segments with closed endpoints only g x f x 5 X

In triangle ABC angle ABC 150 AB 3sqrt 3 and BC 4 The line through A that is perpendicular to AB and the line through C that is perpendicular to BC meet at D Find the area of quadrilateral ABCD