2D Geometry Questions and Answers

Major arc JL measures 300 300 M K Which describes triangle JLM Oright obtuse O scalene O equilateral

What is the equation of the line that is parallel to line y 3x 8 and passe through the point 2 9 Oy 1 3x 2 30 Oy 3x 11 Oy 3x 3 Oy x 53 29

What is the perimeter of kite OBDE O 12 units O 22 units 38 units O 58 units A 24 C 10 E 6 B

Given ZAOB is a central angle and ZACB is a circumscribed angle Prove AACO ABCO C A B O We are given that angle AOB is a central angle of circle O and that angle ACB is a circumscribed angle of circle O We see that AO BO because We also know that AC C since Using the reflexive property we see that Therefore we conclude that AACO is congruent to ABCO by the

O x 2 y 2 25 O x 2 y 2 25 x 2 y 2 5 21 5 4 6 8

What are the coordinates of the center of the circle represented by the equation x 3 y 4 25 3 4 3 4 3 4 3 4

What is the standard circle equation from the general circle equation x 8x 144 12y O x 4 y 6 196 O x 4 y 6 2 196 O x 4 y 6 144 O x 4 y 6 144

Find the center and radius of the circle with the given equation x 5 y 9 16 5 9 16 5 9 4 5 9 16 5 9 4 Question 14 1 point Write the equation of the circle centered at 2 1 and tangent to y 1 O x 2 y 1 4 x 2 y 1 1 O x 2 y 1 4 x 2 y 1 2 CXR

To prove the circles are similar which sequence of transformations will map circle A with center 3 8 and radius 6 to circle M with center 1 4 and radius 2 Translate 4 4 then dilate by scale factor of 3 Translate 4 4 then dilate by scale factor of 1 2 Translate 4 4 then dilate by scale factor of 1 3 Translate 4 4 then dilate by scale factor of 2

What is the radius of circle 2 2 x 8y y 2x 8 5

What is the center of the circle with the equation 12 y 6y 4x x 2 3 6 4 2 3 6 4

11 When graphing one variable data is the frequency the dependent or the independent variable 1 mark

3 Write a proportion you could use to find the value of a 3 Ex 1 2 9 1 a

of the right triangle shown at the right 4 2 Ex 20 42 ype a response Show Your Work

DC 0 In circle I if BG 17 and mCHA 256 10 find each measure MIN B F E H BC FB mAB mBC mEC

Uses circular corkboards to make 18 watermelon coasters to sell at a craft fair 31 He paints one side of each coaster with special paint Each jar of paint covers 200 in Will one jar of paint be enough to paint all the coasters 32 He puts decorative tape around the edge of each coaster How much tape does he need for each coaster 8 in 72

5 29 What is the area of the segment 10ft Q M N 30 T 5m A B 144 30 Round to two decimal places

33 Error Analysis Luke was asked to compute the length of AB What is Luke s error S 1 5 radians A n 360 1 5 360 2Ttr 2 3 3 B

Directions Find each angle and arc measures 1 M 21 N K L 5 2 3 4 1 mJK mZJNM mKL mJKM mMKL 2 72 W S T 87 X V U 7 6 m UXV mST mWV mTW mTVW 8 9 10

Find x 76 N X 6x 20 Y Type a response If MP 5x 34 and PN 2x 4 find MP K M 3 GN

Directions Find each value or measure 11 U R 15x 26 T S 26 X 12 18x 2 E D 15 H G F 103 X

Degrees Radians Radians Degrees Directions Convert each measure to radians 17 30 18 20 5 150 Directions Convert each measure to degrees 4T 21 3 5A 36 19 220 7A 22 4 N

If DE 11x 15 and FG 32x 27 find DE D H E G 8 Find mMP 8 9x 43 N M 5r 33 P

f x 10 7 subtract 9 take reciprocal multiply by 2 subtract 9 take reciprocal multiply by 2 subtract 9

8 Graph the transform function on the same graph as its parent function a f x x 3 2 b f x 2x 31 5 10 104

Use transformations of the standard cubic function f x x to graph the function h x 5x Use the graphing tool to graph the function Click to enlarge graph For any answer boxes shown with the grapher type an exact answer 0 8 6 4 2 10 8 6 4 2 2 Ay 4 6 8 0 8 10 A

Establish the identity cos 8 tan 8 cot 8 csc 8 Write the left side in terms of sine and cosine cos B Simplify the expression inside the parentheses from the previous step and write the result in terms of sine and cosim cos 8 Simplify the expression from the previous step and write the result in terms of sin 8 The fraction from the previous step then simplifies to csc 8 using what OA Pythagorean Identity OB Cancellation Property OC Even Odd Identity OD Quotient Identity al Identit

4 Imagine that the Consumer Price Index for Canada in 2020 was 102 6 Assume a base year was established in 2006 a What can you conclude about prices in Canada in 2020 1 mark b If a set of tires cost 440 in 2006 how much would the same set of tires cost approximately in 2020 2 marks

Type the correct answer in the box A printer creates a right triangular card where the hypotenuse h is three times as long as the shorter leg What is the length of the longer leg I in terms of h Write the answer in simplest form by replacing a b and c with the correct values 1 0 101 Vo 4 a bh X S 2 TE a e 9 sin cos tan sin cos tan AP CSc sec cot log log In 11 0 L ZAN U 0 00

PLE 3 For each quadratic function find the axis of symmetry of its graph 10 y 3x 18x 1 9 y x 4x 7 11 y 2x 3x 4 12 y 3x x 5

Find the axis of symmetry of each parabola 6 7 9 2 4 2 8

res of the following angles in the isosceles trapezoid 74 2 3 37

If the point 20 23 is on the graph of y g x which one of the following points must be on the graph of y g x 7 27 23 O 20 30 13 23 O 20 16 O 16 19

Jai spots an airplane on radar that is currently approaching in a straight line and that will fly directly overhead The plane maintains a constant altitude of 5375 feet Jai initially measures an angle of elevation of 15 to the plane at point A At some later time he measures an angle of elevation of 30 to the plane at point B Find the distance the plane traveled from point A to point B Round your answer to the nearest foot if necessary

A boat is heading towards a lighthouse where Dalvin is watching from a vertical distance of 138 feet above the water Dalvin measures an angle of depression to the boat at point A to be 13 At some later time Dalvin takes another measurement and finds the angle of depression to the boat now at point B to be 45 Find the distance from point A to point B Round your answer to the nearest tenth of a foot if necessary

Find mZEOF for Oo mZEOF Simplify your answer COLL G To 0

X Simplify your answer x 60 R 4x 60 A P 3x 8

The length of the arc is m Simplify your answer Type an exact answer in terms of x CIT 9m

An outlier is an extreme value that is significantly less or more than the rest of the data In the data below take out the outlier then calculate using a statistics calculator or spreadsheet the standard deviation of the heights of 15 soda cans 92 8 92 8 92 9 92 9 92 9 92 8 92 7 92 9 92 1 92 7 92 8 92 9 92 9 92 7 92 8 Round to the nearest 100th

If 100 then the area under the curve to the right of ui 100 10 50

Students at Roseville High School took an IQ test with a mean of 100 and a standard deviation of 15 Approximately 95 of the IQ scores are between and

The sum of the deviation about the mean for a whole data set is

Choose the three characteristics of a Normal Distribution Select one or more a Symmetrical b The standard deviations are limited to three C Total Area under the curve is 1 d Data is grouped to the right e Bell Shaped Curve

Using the rules of standard deviation if a value is with in standard deviations of the mean it might be considered a new discovery or incredibly rare standard deviation of the mean then it is 68 likely to occur If data is

The variance x x 17 15 23 7 9 13 is 3 of the data n l

W X 109 N Y What is the measure of angle WZY O 54 5 O 71 O 125 5 O 180

O E B D Use the diagram to complete the statements The measure of angle EJB is measure of angle BOE The measure of angle BDE is measure of angle BOE The measure of angle OED is measure of angle OBD the the the

A 60 C O B Which statements are true Check all that apply O MCB 120 mcB 60 OmZCOB 2 m CAB OmZCOB 120 Om COB B m CAB

If the measure of arc QP is 76 degrees and angle 3 is 92 degrees what is the measure of arc SR

7 In circle A below AC 1 and m BAD 70 What is the arc length of BC d C a b 7T 117 18 36 7 117 36 18 D B A