2D Geometry Questions and Answers

11 The diagram shows the shape of one hole at a mini golf course The course is being renovated and the grass surface replaced Find how many square feet of grass will be needed to cover this area If the wooden railing along the outside also needs to be replaced how many feet of railing will be needed 12 The mini golf course has several holes with the same shape just a different size Write polynomials that can be used to calculate the amount of grass and railing needed for any course that shape 13 The mini golf course has another generic shape used for several holes write a polynomial for the area and perimeter of this shape as well 3x 7 ft 14 7 ft 2x 7 ft 14 ft x ft ft x ft 7 ft DE x ft 2x ft x ft x ft 2x f

10 Reflect the ant over the line y x 2 Create anchor points as needed 2 4 2 0 2 4 2 pre image

12 g x 2x 3 5 0 5 5 13 State at least one similarity and one difference between the functions for

Perform each of the transformations as described Focus on anchor points 9 Translate the grasshopper right 4 and up 3 2 20 0 2 2 3

20 Construct compass and straightedge AEFG F G Please don t answer jost try to explay

R 4x 3 X M 14 a What is the value of x 6x 12 b What is the length of RM 2X 15 c What is the length os RS 66 3x 1 X N 15 a What is the value of x M b What is the lenghth of MY c What is the lenghth of XY is Ray 5x48 8x 24 M 16 a What is the value of x b What is the length of XM c What is the length of XY 9x 12

Dir 13 P 5x 3 M 11 2x Q a What is the value of x b What is the length of PM What is the length of PO

CONNECTING CONCEPTS Point S is between points R and I on RT Use the information to write an equation in terms of x Then solve the equation and find RS ST and RT a RS 2x 10 ST x 4 RT 21 6 Equation X b RS x 9 ST 19 RT r 14 Equation X A CONNECTING CONCEPTS In the diagram AB BC AC CD and AD 12 Find the lengths of all segments in the diagram AB BC RS ST BD a AC RS ST RT B D

The figure below is a right triangle with side lengths t u and v Suppose that m LT does not equal m ZU U V Complete the following 21 sin T Part 1 In A TUV LT and ZU are Choose one Part 2 Use t u and v to fill in the blanks Make sure to use the appropriate upper case or lower case letters sin U 8 T cos U cos T Part 3 Select all of the true statements sin T cos U cos T cos U sin T sin U cos T sin U None of the above is true Part 4 Fill in the blank sin 46 cos

Given the figure below find the values of x and z X Z 13x 5 7x 31 X 20 S

For the following exercise perform the indicated operations and express the result as a simplified complex number 5 2i 4 i

Find the slope of a line perpendicular to each given line y 6x 1 y x 1 3 y x 2 4

Find the slope of a line parallel to each given line y 2x 3 y y 3x 4 5

5 1 0 1 point E 2 A C 30 10 Solve for y Oy 6 67 Oy 5 y 9 y 6 y B

1 point 25 10 A 2 5 C Segments AB and BC are both tangent to the circle shown above What is the length of BC Note photo not necessarily to scale 5 5 B

W 3 Z The measure of arc XY is 85 degrees The measure of arc WZ is 25 degrees What is the measure of angle 3 60 degrees 12 5 degrees 30 degrees 42 5 degrees

2 1 point R 102 EF m is T What is the measure of arc RT 156 degrees 102 degrees 88 degrees 204 degrees

Show that the equation represents a circle by rewriting it in standard form 3x 3y2 6x y 0 Find the center and radius of the circle x y r

8 If BD BC BD 5x 26 BC 2x 1 and AC 43 find AB A 43 D 5x 26 24 1 B C

15 Find x if m22 4 7x and m2HFG 11x 10 16 Find x if m2l 4x 3 am m22 3x 7

13 Find x if mz1 6x 1 and m RTS 10x 4 S R

Each segment below is being bisected Find the requested measurements 17 Find FE and DE 29 5 TI F E 18 Find UT and ST S 3 6 U

Find the area of this shape

Let G be a connected graph with k 0 vertices of odd degree i Show that the minimum number of trails that together include every edge of G and that have no edges in common is k 2 ii How many continuous pen strokes are needed to draw the diagram in Fig 6 8 without repeating any line

Find the midpoint of the line segment with the given endpoints 5 6 1 2 5 6 4 3 1 6 7 5 4 6 3 9 11 10 3 9 8 4 3 5 5 10 8 2 9 8

2 The diagram is a straightedge and compass construction Lines m and n are the perpendicular bisectors of the sides of triangle ABC Select all the true statements A E A Point E is closer to point A than it is to point C B Point L is closer to point B than it is to point A C Point D is closer to point B than it is to point C D Point J is closer to point A than it is to point B or point C E Point K is closer to point C than it is to point A or point B F Point L is closer to point C than it is to point A or point B OF

the figure below O is between Mand P and N is the midpoint of MO If NO 6 and NP 8 find MP

the scalar equation of the plane containing the following 3 points P 2 1 3 Q 1 1 1 R 1 2 3

1 12 points A particle traveling in 3D space has the following position r t t t 1 1 at time t Consider the vector 2 3 0 a At what time s t is the particle traveling in a direction parallel to b At what time s t is the particle traveling in a direction perpendicular to u

8 Name all pairs of congruent segments in KLMN Use the congruence symbol to write your answer 9 M 4 8 is the midpoint of DE D has coordinates 6 1 Find the coordinates of E KM KL NL M2 For Exercises 10 and 11 use a ruler to draw each figure Label the figure and mark the congruent parts 10 AB and CD with M as the midpoint of both AB and CD AB 6 4 cm and CD 4 0 cm A B and C are not collinear 12 Sketch six points A B C D E and F no three of which are collinear Name the lines defined by these points How many lines are there E 11 AB and CD C is the midpoint of AB with AC 1 5 cm D not on AB is the midpoint of AE with AD 2BC B 13 In the figure below B C H E is a set of four coplanar points Name two other sets of four coplanar points How many sets of four coplanar points are there F 8 cm H 8 cm Cube M

Your answer is incorrect In the figure below mz WXZ 113 and m2 2 is 7 more than mz 1 Find mz 1 W X 2 m 21 X

Quadratic Functions 1 Here are 4 equations of quadratic functions and 4 sketches of the graphs of quadratic functions A y x 6x 8 B y x 6 x 8 C y x 6 8 D y x 8xx 6 a a x 2 Match the equation to its graph and explain your decision Equation A matches Graph because Equation B matches Graph Equation C matches Graph Equation D matches Graph because because 3 because 4 b Write the co ordinates of the points P Q R 2 The graph of a quadratic function has a y intercept at 0 5 and a minimum at 3 4 Write the equation of its curve function S S

the figure below mz WXZ 113 and mz2 is 7 more than mz 1 Find mz 1 W X 2 Y mz1 0

Q3 Sharon is remodeling the floor her studio apartment and needs to know how many square total area is for this apartment The figure below shows the layout of the floor Polynomial lox 3x 4 2x x3 3x 4 x 1 3x 4 x 2x 5 4x 6 c If x 6 then what is the total square footage of the studio apartment 510 d If flooring will cost 35 per square foot then how much will she have to pay Q

2x 3 2 Find the area of the composite figure X 4x4 X 4

Calculator Which equation represents the function on the graph f x sin x f x cos x f x sin 2x f x cos 2x O O 3 K24 2 AA 2 3 KIN 74

Consider the function f x y x y Which of the following graphs is the graph of a level curve of f x y Select all that apply 04 x y 0 Oy x 1 x y 1 O z x 1 O z y 1

Solve AABC a 3 2 cm c 2 6 cm and ZA 46 Begin by sketching and labellin a diagram Account for all possible solutions Express each angle to the nearest degree and each length to the nearest tenth of a unit

Select the graph of the function and its parent function g x x 4 O 4 2 y 24x y 11 Describe the transformation The graph of g is a translation unit s of the parent function

Tree height feet Tree Growth 6 4 2 0 0 6 2 4 Age years X Use the graph to write an equation of the line y Interpret the slope A The height increases 2 3 feet each year B The height increases 1 5 feet each year C The height increases 1 foot every 1 5

Look at the diagram and evaluate Which of the statements below is TRUE I J K L 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Answer IK JL IJ JK IL JK I is the midpoint of IK Submit Answer

Find the value of x Hint The sum of the angle measures of a quadrilateral is 360 X Simplify your answer 2x 30 4x

4 State whether the following graphs are even odd or neither Determine their symmetry x axis y axis origin or none Select all of the following graphs which are one to one functions 03 a d 2375 3432 b e C f

Find the points of intersection of the following pair of curves y x 5x 5 y x 7x 9 Select the correct choice below and if necessary fill in the answer box to complete your choice OA The intersections are Type an ordered pair Use a comma to separate answers as needed OB There are infinitely many solutions of the form x x where x represents all real numbe OC There are no points of intersection

2 Translate the following statements into coordinate points a f 1 1 c g 1 1 b h 2 7 12 d k 3 9 9

Are the given rectangles similar 3 12 91 5 Select one a No O b Can not be determined OC Yes 20 Based on the diagram below we can say that tha 11 91

Perform a curve discussion of the following function f x x 4x x 2 To do this carry out the following steps and briefly justify the individual results a Maximum definition range b symmetry f x f x oder f x f x c Poles or definition gaps d limits e derivatives f x f x f x f Zeros of the function and the first three derivatives f x 0 f x 0 f x 0 f x 0 g Extreme points high or low points maximum minimum h Turning or saddle points curvature behavior

Show Transcribed Text Construct a certain circle Begin with three independent points Label them A B and C if they are not already labeled that Construct the point D that is the base of the altitude at A Construct the circles B that is centered at B and goes through D Let B intersect AB at P Construct the circle C that is centered at C and goes through D Finally construct the circle that is tangent to B at P and is tangent to C Highlight this last circle by coloring it a unique color

Find the equation for the hyperbola whose graph is shown 30 20 10 30 20 10 10 20 30 F 0 17 10 20 F 0 17 30

Use the graph of f x 2 to obtain the graph of g x 2x 3 2 OA AY E O C OD Q