2D Geometry Questions and Answers

Rewrite the equation of the circle x 12x y 3y 44 in standard form x 6 x 4 36 x 12 x 8 36 x 6 x 4 8 x 12 8 8

The quadrilateral ABCD is a square What is the area of the square given the vertices are A 4 3 B 1 4 C 2 1 and D 3 2 O A 3 2 1 D B C 25 square units 26 square units 26 square units 4 26 square units

If you are given a radius and asked to find the diameter what do you do ultiply the radius by 2 Take the square root of the radius Divide the radius by 2 Square the radius

Triangle ABC has vertices A 3 4 B 5 2 and c 1 2 6 Ka A R 19 A 3 4 W C 1 2 B 5 2 Which equation could be used in proving the triangle is isosceles O 5 3 2 4 1 3 2 4 O 1 5 2 2 1 3 2 4 1 3 2 4 20

Find the area of the rectangle ABCD with vertices A 3 0 B 3 2 C 4 1 and D 2 3 A 3 0 54 3 2 1 D 2 3 4 50 3 5 B 3 2 1 2 3 4 5 C 4 1 18 square units 20 square units 40 square units square units

Which graph below best describes the circle x 2 1 4 b

Find the point I that is on the directed segment of that is the distance from G to H given a 4 1 and point 3 4 G O 23 0 0 5 2 3 O 1 26 1 2

42 21 84 Find the measure of arc NL 45 42

Which statement is true about equations of perpendicular lines The slopes of the two equations must have signs that are opposite The slopes of the two equations must be the exact same The y intercept of the two equations must be the exact same The slopes of the two equations must be negative reciprocals

Which equation below would be parallel to the line y 2x45 and pass through the point 3 1 Or 1 1 y 2247 y 2x 1 y 2x 5

What is the equation of the line with a slope of and passes through the point 1

Question 2 4 points Which line graphed below has a slope of 0 tien 4 points

Question 4 12 5 points Each person standing in a comfortably crowded area requires 2 5 square feet of floor space 560 people 890 people 1440 people 2400 people A manager at a mobile phone store will be holding an event in which she will be giving away a couple of the latest Y Phones She needs to know the maximum capacity of the number of people in a crowd that can fit in her parking lot if all the cars were removed 40 ft Use the dimensions provided in the aerial diagram of her store s parking lot shown at the right to determine how many people the lot could hold if each person would require a minimum of 2 5 square feet 50 ft 120 ft Mobile Phone Store 20 ft

An orange farmer in Florida has determined that he needs a 1100 square feet of land for every 3 orange trees The farmer has a total of 520 orange trees on his farm Based on the information provided determine approximately how much land is needed for his orange trees in acres 1 acre 43560 square feet 2 6 acres 4 4 acres 12 3 acres 19 1 acres GY

78 O S 102 19 5 Determine the measure of Z 78

Which geometric shape would be best to use to estimate the volume of the earth contained in the mountain shown at the right prism cone hemisphere cylinder

radius diameter What part of the circle is present chord secant

Q3 In the diagram A B C are points on the circumference of a circle and O is the centre of the circle Q4 A Find the size of angle ABC giving reasons for your answer In the diagram 316 C N so of a circle and the line AR is the C 2

Q11 A03 The lines AB BC and AC are tangents to the circle and O is the centre of the circle Given that the area of the triangle is 452 54m2 find the radius of the circle to 1 decimal place 32m 40m 28m 4

Q6 A B C and D are points on the circumference of a circle and O is the centre of the circle B A ind the size of angle x giving reasons for your answer D 112 2

A B C and D are points on the circumference of a circle and O is the centre of the circle The line EF is a tangent to the circle A B O D 66 Given that the angle BAD has a value of 2x find the value of x

Q2 A B C and D are points on the circumference of a circle 82 B D a Find the size of angle x giving reasons for your answer 82 because the opposite angles of a quadrilateral inscribed in a circle are supplementary a Find the size of angle y giving reasons for your answer 2

Q10 A03 A B and C are points on the circumference of a circle and O is the centre of the circle The lines AB and AC are tangents to the circle is a tangent to the circle A 72 CO B 10 15cm Calculate the length AO giving your answer to 1 decimal place

egments with endpoints on a circle are called

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