2D Geometry Questions and Answers

Given the diagram of the spinner describe how to change each sector of the spinner so that each of the outcomes A B C or D is equally likely A B C

Bonus Use the figure below to find the measures of the angles 1 2 7 3 4 5 6 7 8 9 54 1 118 96 2 4 5 28 79 24 8 9

5 4 6 Statements 1 2 22 Given FJGH is a rectangle Prove FH JG Use the bank below FGH and JHG are right angles 3 SALA FG JH SAS Reasons 1 2 FLUENIT 3 All right angles are congruent 4 5 6 F they are even Side Reflexive Property K 8 H

Given a segment with endpoints 10 3 and B 5 3 Find the coordinates of point CpM AC 2 between A and B so that the ratio CB 3 A 1 3 B 4 3 9 0 3 5 3

A tree casts a shadow that is 22 feet long at the same time a 4 foot fence post casts a shadow that is 3 5 feet long Use similar triangles to find the length of the tree A B C D 15 7 feet 19 3 feet 25 1 feet 63 6 feet

If the cos 60 1 2 A B 2 3 2 2 3 C D 2 find the sin 30

What similarity criterion can be used to prove AABC AAED A D B AA acc D Ten ST

ve for pe2 monoH noitatibo a era lot to pinW 1 H A 3 B 4 C 9 L

Find the equation of the parabola described below Find the two points that define the latus rectum and graph the equation focus at 0 2 vertex at 0 0

A card is drawn from a deck of playing cards What is the probability of drawing a heart or the King of Spades

Drawing a diamond from a deck of cards drawing an 8 from a deck of cards O Overlapping Mutually Exclusive

A card is chosen from a standard deck of 52 cards What is the probability that the card chosen is a spade or a seven

A bag contains 2 yellow balls 3 green balls 5 red balls and 6 black balls What is the probability of drawing a yellow or red ball if only one ball is drawn

Drawing a face card from a deck of cards drawing a 5 from a deck of cards O Overlapping O Mutually Exclusive

A basket contains three apples three peaches and four pears You randomly select a piece of fruit What is the probability that the fruit you choose is an apple or a peach

Rolling an odd number on a die rolling a 2 on a die O Overlapping Mutually Exclusive

Solve for x Assume that lines which appear to be diameters are actual diameters 16x 4 70 For your answer only put the number Do not type x R 42 Question 39 1 point Find the missing angle measure in the circle For lines that look like diameters can be assumed as the diameter for the circle 96

Vertices at 0 8 and 0 8 asymptote the line y 2x An equation of the hyperbola is 0 0 1 Use integers or fractions for any numbers in the equation Which of the following is the correct graph O A 13 13 OB 13 14 13 43 13 Q O C 13 13 13 13 OD Ay 13 H 13 13

Find the standard equation of the parabola whose vertex is 6 6 and whose directrix is y 4 Also find the focal diameter of each parabola The standard equation of the parabola is Simplify your answer Use integers or fractions for any numbers in the expression The focal diameter of the parabola is Simplify your answer XI

5 Find the area of the quadrilateral 5 100 8 6 7

Fencing with the length of 420 meters surrounds two identical playing fields with a common side The fields can be side by side and separated by a fence as shown in the figure Find the dimensions and the maximum area of each field The larger dimension of each field is meters The smaller dimension of each field is meters

Determine the standard equation of the ellipse Vertices at 2 3 and 4 3 focus at 3 3 Choose the correct equation below OA O C x 1 y 3 9 5 x 1 y 3 5 9 1 1 Next question OB x 1 2 y 3 9 5 1 OD x 1 y 3 1 5 9

Determine the sum Find the answer in simplest form 1 1 1 x 1 Enter the simplified sum in the box N Show Hints I

Write an equation of a line tangent to the graph 3x 3y2 75 at the point 4 3 4 0 v 3x 25 O X 4 O y x 1 7 7 O y x 3 4 O y x 25 3 3

An isosceles triangle ABC has legs of lengths 24 and a vertex angle that measures 36 degrees Determine the length of it s base BC to the nearest length

Find the exact value of arcsin 1 O arcsin 1 2 370 O arcsin 1 TU O arcsin 1 1 2 O arcsin 1 35

4 A bird is perched on top of a pole on a steep hill and an observer is located at point A on the side of the hill 110 m downhill from the base of the pole as shown in the figure The angle of inclination of the hill is 50 and the angle a in the figure is 9 Find the distance from the observer to the bird 110 m

and the eccentricity e and the distance d from the pole to the directrix of the conic 2 sin 8 4 Sketch and identify the graph Use a graphing utility to confirm your results 2 O q 1 1 1 24 1 D 6 4 2 n 2 2 8 2

Solve the equation for exact solutions in the interval 0 360 Use an algebraic method 4 sec 20 tan 0 8 tan 0

18 The first floor of a house is shaped like a rectangular prism and the second floor is shaped like a triangular prism The dimensions are shown on the following diagram If a 1000 BTU air conditioner can cool a house with a volume of air up to 1000 m3 can this air conditioner cool the house sufficiently 5 marks 14 m 4m Am

Find the area in square centimeters of a regular pentagon with an apothem of length a 4 4 cm and each side of length s 6 4 cm Use the formula A cm

Three atoms with atomic radii of 4 0 5 0 and 6 7 are arranged as in the figure Find the measure of the angle at the center of atom B inside the triangle CID 40 A 67

Find the area of the circle given in the figure Use 3 14 O 103 cm O 1017 36 cm O 507 3 cm 300 cm 18 cm

After a big rain the area of the surface of the local reservoir was 576 acres ac Use the facts to find the area of the surface of the reservoir in square miles mi 2 mi X Conversion facts fo 1 acre ac 43 560 1 square mile mi 640 acre 1 hectare ha 2 5 acres Note that means is approximat For this problem treat

following quadratic trinomial x 20x 100

O Factor the following quadratic trinor x 3x 18

below Show all steps for full credit no exceptions a 13 12 37

4 Simplify the following expression x 8

In circle M M N 2 and the length of NO T Find m N MO M N

What are the slope and y intercept of a line that is perpendicular to line y 3 and passing through point 4 20 Om and b 28 Om 5 4 and b 29 Om and b 25 5 Om 5 4 and b 32 Previous Page Next Page Page

Question 10 1 point Which of the following is the most precise classification of the quadrilateral given points A 4 4 B 1 2 C 4 2 and D 7 2 O trapezoid none square Oparallogram Previous Page Next Page Page 10 of 13

Question 4 1 point Triangle RST has coordinates R 1 7 S 3 1 and T 9 2 Is this a right triangle Prove your answer why or why not No this is not a right triangle because none of the slopes are negative reciprocals of each other O Yes RS is perpendicular to ST because their slopes are negative reciprocals of each other Yes RT is perpendicular to ST because their slopes are negative reciprocals of each other RS is perpendicular to RT because their slopes are negative reciprocals Yes of each other

In circle U mZPOQ 130 and the length of PQ 37 Find the length of OP P 0 Q

The coordinates of the vertices of ACAT are C 2 3 A 8 2 and T 4 5 Which type of triangle is ACAT acute right isosceles obtuse

Question 4 1 point What is the equation of the line that is perpendicular to line y 1 5x 1 and crosses point 2 4 y 5x 15 y 5x 22 y 5x 14 y 5x 23 Previous Page Next Page Page 4 of 13

Determine and state the area of Right Triangle PQR whose vertices have coordinates P 2 5 Q 3 5 and R 6 1 35 25 45 15 Previous Page Next Page Page 10 of 13

Quadrilateral GRAM has vertices G 2 3 R 7 10 A 9 4 and M 4 3 Prove that GRAM is a parallelogram Quadrilateral GRAM is a parallelogram because GR MA and RA MG O Quadrilateral GRAM is a parallelogram because RGM GMA and ZRAM ZGRA Quadrilateral GRAM is a parallelogram because GR RA and MA MG O Quadrilateral GRAM is a parallelogram because MGGR and RA MA

Rectangle JOKE has diagonal endpoints J 5 10 and K 0 2 and diagonal endpoints O 0 10 and E 5 2 What is the area of rectangle JOKE Previous Page Next Page Page 7 of 13 A

Calculate the perimeter of the above triangle 17 1 units 22 9 units 30 units 10 units

The coordinates of the vertices of parallelogram CDEH are C 5 5 D 2 5 E x y and H 8 1 What coordinates of E would make CDEH a paralellogram 2 2 2 2 1 1 3 2