# Geometry Questions

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Geometry
2D Geometry
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
Geometry
2D Geometry
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
Geometry
Coordinate system
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
Geometry
Coordinate system
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
Geometry
2D Geometry
What is the Axis of Symmetry of the following parabola y x 8x 20 Ox 4 X 4 Ox 8 x 8
Geometry
3D Geometry
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
Geometry
Coordinate system
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
Geometry
2D Geometry
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
Geometry
2D Geometry
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
Geometry
2D Geometry
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
Geometry
2D Geometry
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
Geometry
Heights & Distances
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
Geometry
2D Geometry
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
Geometry
Vectors
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
Geometry
2D Geometry
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
Geometry
Coordinate system
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
Geometry
Coordinate system
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
Geometry
Coordinate system
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
Geometry
2D Geometry
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
Geometry
2D Geometry
find the missing angle with a question mark 30 40 50 20
Geometry
Area
3 1289 X y
Geometry
Solution of triangles
10 cm Find the area 18 cm 17 cm 21 cm A cm A b h
Geometry
Coordinate system
5 N X y Z W 64 yo x q wo
Geometry
Coordinate system
In 1 8 Find the value of all variables 1 110 X y 2 10 x y
Geometry
Solution of triangles
6 133 X y Z to Z 20
Geometry
Solution of triangles
3x 5 2x 8x 20
Geometry
Solution of triangles
3y 18 9x 54 y 12
Geometry
2D Geometry
4 x y Z to 55
Geometry
Solution of triangles
9 X 2x 2X 6
Geometry
3D Geometry
4 Almost everyone has played the rock paper scissors game at some point Two players face each other and at the count of 3 make a fist rock an extended hand palm down paper or a V with the index and middle fingers scissors The winner is determined by these rules rock smashes scissors paper covers rock and scissors cut paper If both players choose the same object then the game is a tie Suppose that Player 1 and Player 2 are both equally likely to choose rock paper or scissors a Give the probability model for this chance process b Find the probability that Player 1 wins the game on the first throw 5 Canada has two official languages English and French Choose a Canadian at random and ask What is your mother tongue Here is the distribution of responses combining many separate languages from the broad Asia Pacific region Language English French Asian Pacific Probability 0 63 0 22 0 06 a What probability should replace in the table Why Other b Find the probability that this Canadian s mother tongue is not English c What s the probability that a randomly chosen Canadian s mother tongue is Asian Pacific or Other
Geometry
Solution of triangles
Geometry
Heights & Distances
Step 1 Given information Player 1 and Player 2 are both equally likely to choose rock paper or scissors in a rock paper scissor game Step 2 a Let a b represent the outcome of the game where a and b are the choices of player 1 and player 2 respectively Let R represent the rock S represents the scissor and P represent the paper The total of 9 possible outcomes of the game will be PossibleA outcomes R R R P R S P R P P P S S R S P S S Each outcome is equally likely to happen with a probability of The probability model will be a b P a b Step 3 b From the above table there are only 3 outcomes player 1 is winning that are R S P R and S P The probability that Player 1 wins the game on the first throw will be computed as Winning outcomes Total outcomes R R 1 9 P Player 1 R P 1 9 R S 19 P R 1 9 P P 1 9 3 0 33 So the probability that Player 1 wins the game on the first throw is 0 33 P S 9 S R 1 9 S P 19 S S 10 9
Geometry
2D Geometry
Provide a trigonometric equation Considering only the space between x 0 and 2 pie the equation must only have solutions at x 1 and x 2 explain your thought process and the work you did to create the equation You may round decimal values to 3 places
Geometry
Coordinate system
Create a single BPMN diagram using the Camunda Modeler of the below process narrative Feature appropriate pools and lanes to represent the different entities participants and the message flows between these entities participants Please label all flows sequences messages Do not use sub processes Canvas is a leading provider of LMS Learning Management Software software Canvas is used by many colleges as a teaching course portal
Geometry
Heights & Distances
n 6 S 1 1 n 2 S 13 80 e Refer to the diagram for question 12 22 Plot a graph of the values of energy y axis against the square of the number of the level i e n on the x axis C
Geometry
Vectors
The distance D between a point Q and a line in space is given by PQ x u D X where u is a direction vector for the line and P is a point on the line a Find the shortest distance between the point Q 9 0 0 and the line passing through the points P 0 0 8 and P 0 1 9 b Find the shortest distance between the point Q 9 0 0 and the line segment from P 0 0 8 to P 0 1 9
Geometry
Solution of triangles
7 Use the universal substitution to find the general solution of the equation 2 cos 3x sin 3x 2
Geometry
2D Geometry
4 PB X P 9 C Y 15 B Z
Geometry
2D Geometry
For 6 and 7 find the coordinates of the circumcenter of the triangle with the given vertices 6 A 2 6 B 8 6 C 8 10 7 D 7 1 E 1 1 F 7 9 D
Geometry
2D Geometry
For 6 and 2 6 B 8 t EX 3x 16 FX 11 K H 3x 1 E For 14 16 explain which segments would need to be perpendicular in order for a segment to bisect the angle 14 16 15 B
Geometry
2D Geometry
Fays or segments intersect in the same point they are called rays or segments For 2 5 the perpendicular bisectors of the triangle intersect at a point and are shown in bold Find the indicated measure 2 BG X A 4 PB B G C 15 N 3 GA 5 HP 17 D 11 X X 15 nter of the triangle with the given vertices
Geometry
2D Geometry
12 P is the circumcenter of AXYZ Use the given information to find PY PX 4x 3 P PZ 6x 11 X D CY E Z
Geometry
2D Geometry
3x 16 M 18 H 19 G N E FX 11 For 17 19 classify the triangle by its SIDES 17 G For 14 16 explain which segments would need to be perpendicular in order for a segment to bisect the angle 14 F 15 16 3x 1 H H 8 D 21 22 F For 20 22 classify the triangle by its ANGLES 20 55 65 M E 80 A 45 25 40 20 120
Geometry
2D Geometry
NG NHZx 3 ed angle A N H
Geometry
2D Geometry
For 8 11 N is the incenter of AABC Use the given inform 8 ND 6x 2 NE 3x 7 NF 10 NK 2x 2 NL x 10 NM M ING 143 NH 2x 3 D 12 P is the circumcenter of AXYZ Use the given information to find PY P PX 4x 3 PZ 6x 11 Z 11 NQ 2x NR 3x 2 G NJ N BJ NM H N SC
Geometry
Heights & Distances
Find the cosecant secant and cotangent of angle A given that a 17 3 and b 13 2 Although it is best to leave the ratios as reduced fractions for the purposes of this question round to 4 decimal places Diagram is for reference only and is not drawn to scale CSC A sec A cot A A C 000 B
Geometry
2D Geometry
Midpoint 14 A 2 1 B 10 7 Midpoint AB AB
Geometry
Coordinate system
Write a function based on the given parent function and transformations in the given order Parent function y H 1 Shift 2 5 units to the right 2 Shrink horizontally by a factor of 3 Reflect across the y axis The function based on the given parent function and transformations in the given order is y 23
Geometry
Coordinate system
For 5 9 if point P lies on the perpendicular bisector of LM explain which segments are congruent and which segmen are perpendicular 5 L M 201 211 N 6 L 211 211 M 7 P M 211 N 211 T 8 L N 211 211 P M
Geometry
2D Geometry
Amplitude 9 3 Period 8 7 6 5 4 Show Transcribed Text 1 24 4 Based on the graph above determine the amplitude midline and period of the function Close 4