2D Geometry Questions and Answers

In a school there are 500 girls and 450 boys What is the ratio of girls to students OA 19 10 OB 10 9 C 9 10 OD 10 19

AABC has coordinates of A 7 3 B 8 2 and C 1 8 Find the coordinates of its image after a dilation centered at the origin with a scale factor of 1 5 OA A 7 3 B 8 2 C 1 8 OB A 4 67 2 B 5 33 1 33 C 0 67 5 33 OC A 10 5 4 5 B 12 3 C 1 5 12 OD A 10 5 3 B 12 2 C 1 5 8

In which figure is the dashed line a line of symmetry OA OB OC OD q 3 A

A transformation whose preimage and image are similar is called a OA translation OB rotation OC reflection OD dilation

Let C be the largest circle centred at 2 0 and 2 inscribed in the ellipse x 1 36 16 If 1 a lies on C then 10 a is equal to E

Calculate the following surface areas and volumes Show your work clearly Write the formulas you are using Find the area to the tenths unless otherwise indicated Hint Use the Pythagorean Th to solve for missing sides of right A s if needed R h 5 11 25 121 1 12 049 145 V 11 6 11 12 01 V 25 1 V 3x 275 91 cm 5 cm SA V 4 SA M S S 12 au 16 25 1 60 2 G SM a1 793 LARI 11 cm 7 5 12 47 60 2 10 03x 8 ft SA 236 8 2 10 8 ft 8 ft 2 m Abase 43 3 m Ahaglebs 3 2 m SA Abase 4Atriangle 4 4 3 4 12 U v b h 2 20 3 4 SA 16 num Abase b 64 V 6 h 3 2 0 08 SA 1 10 22 4 10 224 100 324 11 20 8 10 83 3 SA 64 4 43 2 64 112 8 236 8 22 4 in SA 3247 V A triangle b5 8 1 8 Goycle 64 10 03 3

Graph triangle RST with vertices R 3 7 S 5 2 and T 3 5 and its image after a reflection over X 3 OA B OC O D Sa ast 9 hat M R 19 R

Find the coordinates of the image of a triangle with vertices A 0 5 B 9 0 and C 6 2 under rotation of 90 clockwise about the origin A A 0 5 B 9 0 c 6 2 B A 5 0 B 9 0 c 2 6 OC A 0 5 B 9 0 C 6 2 D A 5 0 B 0 9 C 2 6

3 Draw the image of the figure after a rotation of 180 around O OA O L B OC O D N N M L O O 0 N L O 0 0 L M L L M M 34 M M N N N

LaKeesha was sitting in seat J1 at a soccer game when she discovered her ticket was for seat D4 Write a rule to describe the translation needed to put her in the proper seat OA x 6 y 3 OB x 6 y 3 OC x 6 y 3 OD x 6 y 3

4 Convert to Standard Form Identify the y intercept then sketch a graph of the function a h x 3 x 2 x 5 vlx 215 2 b y 2 x 7 x 2 c f x 4 x 2 2

A change in a geometric figure s position shape or size is called a an O A isometry B preimage C image OD transformation

A transformation in which the preimage and image are congruent is called a an O A isometry OB identity OC equal transformation OD congruent transformation

The original figure in a transformation is called the OA polygon OB preimage OC isometry

To approach the runway a small plane must begin a 9 descent starting from a height of 1125 feet above the ground To the nearest tenth of a mile how many miles from the runway is the airplane at the start of this approach 1125 ft 9 Not drawn to scale O 1 3 mi A O 0 2 mi B O 7 191 5 mi C O 1 4 mi

A captain of a sailboat sights the top of a lighthouse at a 17 angle of elevation A navigation chart shows the height of the lighthouse to be 120 meters How far is the sailboat from the lighthouse O 410 44 m A O 50 22 m B O 36 69 m C 392 50 m

3 In AXYZ ZY is a right angle and sin X Find cos X in fraction and in decimal form Round to the nearest hundredth if necessary X OA 1 25 OB 0 75 OC 5 OD 1 67 0 6

If x y 2 then Z represents Select one O a O b the diameter of a circle the radius of a circle c none of the above d one coordinate of the midpoint

Find the value sine given that c 10 and a 6 A a OA OB C 355 45 4 b

Find the value of each missing variable H I 5 60 y 60 8 30 Hypote y X 14 y 20

Atland Draw a picture then so A roofer leaned a 16 foot ladder how high up the house does the

A To satisfy safety reg the distance from the v base of a ladder should loas

9 An angle bisector of a triangle divides the opposite side of the triangle into segments 8 cm and 2 cm long A second side of the triangle is 4 9 cm long Find the longest and shortest possible lengths of the third side of the triangle Round answers to the nearest tenth of a centimeter OA OB OC 16 cm 1 2 cm OD 19 6 cm 1 2 cm 39 2 cm 3 3 cm 39 2 cm 19 6 cm

8 Find the value of the variable s If your answer is not an integer leave it in simplest radical form Not drawn to scale 17 OA x 17 3 v 34 OB x 34 y 17 3 OC x 34 3 y 17 OD x 17 y 34 3

A set of nonzero whole numbers a b and c that justify the equation a b c is called OA OB a Pythagorean Double a Pythagorean Triple

If a ray bisects an angle of a triangle then it divides the opposite side into two segments that are OA OB OC bisectors OD proportional congruent perpendicular to the other two sides of the triangle

Find x to the nearest tenth 18 8 Not aan to scale OA OB OC OD 1 4 28 6 4 5 12 3

Use the Side Splitter Theorem to find x given that PQ BC K B OA OB OC OD 12 12 6 24 20 18 C

Find the length of CN in the triangle below where MNAC OA OB OC D 18 24 13 5 4 5 8 B

The Geometric Mean of two positive numbers a and b is OA OB OD X ab B X ab ela ale 11

Jason wants to walk the shortest distance to get from the parking lot to a How far is the spot on the beach from the parking lot b How far will his place on the beach be from the refreshment stand Beach OA OB OC OD 30 Refreshment Stand 40m Parking Lot 38 m 12 m 34 m 16 m 24 m 18 m 24 m 32 m

7 Are the triangles similar If so explain why 30A OA OB OC OD 4 6 yes by AA yes by SAS yes by SSS The triangles are not similar

Find the length of the altitude drawn to the hypotenuse The triangle is not drawn to scale OA OB OC 24 80 4 5

5 Solve for x The figure is not drawn to scale 10 OA OB OC OD 6 x 50 3 x 8 8 3 25 6 X x 6

x 1 y 4 16 1 0 0 4 4 0 0 1 Question 15 1 point To prove the circles are similar which sequence of transformations will map circle A with center 5 4 and radius 18 to circle M with center 2 3 and radius 6 DO Translate 3 7 then dilate by scale factor of 3 Translate 3 7 then dilate by scale factor of 1 3 Translate 3 7 then dilate by scale factor of 3 Translate 3 7 then dilate by scale factor of 1 3

Which of the following points is on the circle whose equation is x 2 y 3 25 0 3 O 2 0 2 3 0 0 0

1 point Convert the equation from Standard to General form x 3 y 2 4 Ox y 6x 6y 14 Ox y 6 6y 4 0 Ox y 6x 4y 9 0 02x 2y 6x 6y 4 0 Previous Page Next Paze

uestion 12 1 point What is the equation of the circle given A is 3 2 and B is 10 2 O x 3 2 y 2 2 49 x 3 2 y 2 2 49 x 3 2 y 2 2 65 x 10 2 y 2 2 49 Previous Page B Next Page Pa

What is the radius of the circle for the equation below Round to the tenths place x y 4x 010 5 4 0 19 04 4 4x 10y 10 0 Previous Page Next Page Page 2 of 13

Question 10 1 point Find the center and radius of the circle with the given equation x 2 y 6 36 2 6 6 2 6 6 O 2 6 36 2 6 36 Previous Page Next Page

The coordinates of three vertices of a rectangle are 4 1 1 3 and 4 3 Which of these points is the fourth vertex OA 1 3 OB 0 3 OC 1 1 D 4 1

Triangle QRS is similar to triangle TUV What is the measure of angle V XSA e OA OB OC OD 70 110 35 250

A circle has the equation x 1 y 3 16 What are the coordinates of its center and the length of its radius 1 3 and 4 1 3 and 16 1 3 and 4 1 3 and 16 Previous Page Submit Quiz Next Page 0 of 15 questions saved Page 6 of 13

What is the center of the circle with the equation 9 y x 2y 6x 6 2 6 2 O 3 1 3 1

The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are DA similar OB corresponding OC congruent OD equal to the original triangle and to each other

Find the geometric mean of the pair of numbers 169 and 4 OA OB C OD 36 26 46 31

is a statement that two ratios are equal A an OA cross product OB extended proportion OC proportion OD ratio

Solve the proporti 3y 8 y 12 5 OA 40 3 OB 10 OC 3 40 OD 7

Are the polygons similar If they are write a similarity statement and give the similarity ratio In AQRS QR 4 RS 15 and m R 36 In AUVT VT 8 TU 32 and m T 36 OA ASRO AUTV 2 15 OB AQRS AVTU OC OD 32 1 ARSO ATUV 2 The triangles are not necessarily similar

Write an equivalent ratic 8 min 12 min OA 2 3 OB 2 12 OC 36 48 OD 8 3