Please help Transformations on a Map

Use the map of the United States and your centimeter cube to do the following transformations. Pay attention to which axis for reflections.

1. Start in Hawaii on the black-dot.

a. Reflect over the y-axis. Color this square blue. What ocean are you
in?

b. Go back to Hawaii. Now, reflect over the x-axis. Color this square green. What states are you in?

2. Start in Georgia on the black-dot.

a. Reflect over the x-axis. Color this square yellow. What states are you
touching?

b. Go back to Georgia. Now, reflect over the y-axis. Color this square black. What state are you in?

3. Start in Ohio on the square that says Ohio.
Describe a translation that would get you to Montana.

4. Start in Louisiana on the black dot. Rotate 90 degrees counter clockwise. Name a state in the quadrant you land in. (Can you name its capital??)

5. Start in New York on the black dot. Translate left 4 and down 3. Then reflect the cube over the x-axis. Color this square purple. What state are you in?

6. Start in south Dakota on the black dot .

a. Reflect over the x-axis. Color this square orange. What state are
you in?

b. Then reflect your cube over the y-axis. What quadrant are you in?

7. Start in Kansas on the black dot. Reflect over the y-axis and then translate your cube 6 right and 2 up. Color the square pink. What state are you in?

8. Start in New Hampshire on the black dot. Describe a way you could get to any square in the state of Texas. You may need to use more than one transformation to do this.

9. Start in Idaho on the black dot. Translate 6 right and 3 down. Now, reflect your cube over the y-axis. Color the square red. What state are you in?

Then describe the translation that would get you back to Ohio.

10. Start in Mississippi on the black dot. Rotate 90 degrees clockwise. What quadrant are you in?

BONUS: Start in North Carolina on the black dot. Reflect over the y-
axis. Translate 5 up and 4 right. Reflect over the y-axis. Translate 4 down. Rotate 180 degrees counterclockwise. Shade the box.

1a.) atlantic

1b.) california

2a.) Tennesee and north carolina

2b.) new mexico

3a.)  Add three and reflect accross the x axis

4.) texas (austin), quadrant 3

5.) alabama

6a.)  texas

6b.) quadrant 4

7.) penslyvannia

8.) reflect accross x and y axis (or rotate clockwise by 180 degrees) then go 8 right and up 3

9.) missouri

9b.) up 1 and right 3

10.) quadrant 3

bonus.) i colored it gray and it's in wisconsin

Step-by-step explanation:

1a.) to reflect over the y axis you keep the y axis but swap the x to a negative

1b.) to reflect over the x axis you keep the x value the same but y's sign is swapped

2a.) I've already explained how to reflect something over the x axis

2b.) I've already explained how to reflect something over the y axis

3a.) ohio lies around (5,3) and montana is around (-5,6)  so to get their just go up (or north?) three and reflect accross the y axis

4.) louisana is around (2,-3) and to rotate 90 degrees clockwise  would make the coordinates (-3, -2) which puts you around Texas

5.) new york's coordinates are around (8,5) to go left 4 and down three puts you at (4,2) to reflect it over the x axis gives you the coordinates (4,-2) which is in alabama

6a.) south dakota is around (-2,5) and to reflect it over the x axis gives you (-2,-5) which is texas

6b.) To reflect (-2,-5) over the y axis gives you (2,-5) which is gives you the fourth quadrant

7.) Kansas is around (-1,2) and to reflect over the y-axis gives you (1,2) and to go 6 right and 2 up gives you (7,4)

8.) new hampshiere is around (9, 6) and to get to texas which is around (-1,-3) so let's flip accross the x and y axis to get (-9,-6), then go 8 right and up 3

9.) idaho is around (-8,5) and to get 6 right gets you (-2,2) and to reflect over the y axis gives us (2,2) which is missouri and to get to ohio would require us to to get to (5,3) which would require us to go up 1 and right 3

10.) mississippi is around (3,-2) and to rotate 90 degrees clockwise puts us at (-2,-3) or (y,-x) which is quadrant 3

bonus.) north carolina is around (7,1), to reflect over the y axis puts us at (-7,1), to go up 5 and 4 right puts us at (-2,5) and to rotate 180 degrees clockwise gives us (2,-5)

hope this helps you out good luck

answer: learning objective(s)

·         describe the creation and use of systems of equations.

·         graph a system of linear equations on the coordinate plane and identify its solution.

introduction

sometimes graphing a single linear equation is all it takes to solve a mathematical problem. other times, one line just doesn’t do it, and a second equation is needed to model the situation. this is often the case when a problem involves two variables. solving these kinds of problems requires working with a system of equations, which is a set of two or more equations containing the same unknowns.

let’s take a look at systems of equations, and see what the graphs of individual equations within a system reveal about the mathematical relationship of the variables.

systems of equations

a system of equations contains two or more linear equations that share two or more unknowns. to find a solution for a system of equations, we must find a value (or range of values) that is true for all equations in the system.

the graphs of equations within a system can tell us how many solutions exist for that system. look at the images below. each show two lines that make up a system of equations (in the graph on the right the two lines are superimposed and look like a single line). how many points in common does each system of lines reveal?

one solution

no solutions

infinite solutions

if the graphs of the equations intersect, then there is one solution that is true for both equations.

if the graphs of the equations do not intersect (for example, if they are parallel), then there are no solutions that are true for both equations.

if the graphs of the equations are the same, then there are an infinite number of solutions that are true for both equations.

remember, the graph of a line represents every point that is a possible solution for the equation of that line. so when the graphs of two equations cross, the point of intersection lies on both lines, meaning that it is a possible solution for both equations. when the graphs of two equations never touch, there are no shared points and there are no possible solutions for the system. when the graphs of two equations lie on top of one another, they share all their points and every one is a possible solution.

graphing as a solution method

graphing equations in order to identify a specific point of intersection is usually not a precise way to solve systems because it is often difficult to see exactly where two lines intersect (unless you are using a computer-based graphing program that allows you to zoom in on a point). however, the graph of a system of equations can still give a good idea of what type of solution, if any, exists. let’s graph a system, and see how it works.

graph the system y = 3x and x + 2y = 4. how many solutions does this system have?

a graph of the two lines y = 3x and x + 2y = 4 shows us that the lines intersect, meaning that there is a single (x, y) value that satisfies both equations. looking at the graph does not tell us exactly where that point is, but we don’t need to know that information here, because the question only asks for the number of solutions.

so a system made of two intersecting lines has one solution. now let’s look at a different situation:

how many solutions exist for the system y -0.5x = 7 and 2y = x − 3?

plotting both equations, it looks like there is no solution—the lines are parallel. to check this finding, we can compare the slopes of the equations. to make that easy, we’ll rearrange the equations into slope-intercept form, or y = mx + b.   that gives us the equations y = 0.5x + 7 and y = 0.5x − 1.5.   yes, the slope of both lines is 0.5, which means the lines really are parallel. they never intersect, so there is no point that lies on both lines, and no solution to the system.

step-by-step explanation:

add 5 subtract 1

step-by-step explanation: