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MATH / The point A(3,3) is reflected across the x-axis to A^{'}. Then A^{'} is translated two units to the left to A^{''}. The coordinates of A^{''} are (x,y). What is the value of x+y? […

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

The point A(3,3)A(3,3) is reflected across the xx-axis to $A^{'}$. Then $A^{'}$ is translated two units to the left to $A^{''}$. The coordinates of $A^{''}$ are (x,y)(x,y). What is the value of x+yx+y? [asy] draw((-7,0)--(7,0),linewidth(1),Arrows); draw((0,-7)--(0,7),linewidth(1),Arrows); for(int i=-5; i<0; ++i) { draw((i,-.5)--(i,.5),linewidth(1)); } for(int i=1; i<6; ++i) { draw((i,-.5)--(i,.5),linewidth(1)); } for(int i=-5; i<0; ++i) { draw((-.5,i)--(.5,i),linewidth(1)); } for(int i=-5; i<0; ++i) { draw((-.5,-i)--(.5,-i),linewidth(1)); } label("xx", (8,0)); label("yy", (0,8)); [/asy]
Plain-text mathematical notation (without MathML)
The point A(3,3) is reflected across the x-axis to $A^{'}$. Then $A^{'}$ is translated two units to the left to $A^{''}$. The coordinates of $A^{''}$ are (x,y). What is the value of x+y? [asy]
draw((-7,0)--(7,0),linewidth(1),Arrows);
draw((0,-7)--(0,7),linewidth(1),Arrows);

for(int i=-5; i<0; ++i)
{

draw((i,-.5)--(i,.5),linewidth(1));
}

for(int i=1; i<6; ++i)
{

draw((i,-.5)--(i,.5),linewidth(1));
}

for(int i=-5; i<0; ++i)
{

draw((-.5,i)--(.5,i),linewidth(1));
}

for(int i=-5; i<0; ++i)
{

draw((-.5,-i)--(.5,-i),linewidth(1));
}

label("x", (8,0));
label("y", (0,8));

[/asy]
Original LaTeX notation
The point $A(3,3)$ is reflected across the $x$-axis to $A^{'}$. Then $A^{'}$ is translated two units to the left to $A^{''}$. The coordinates of $A^{''}$ are $(x,y)$. What is the value of $x+y$? [asy]
draw((-7,0)--(7,0),linewidth(1),Arrows);
draw((0,-7)--(0,7),linewidth(1),Arrows);

for(int i=-5; i<0; ++i)
{

draw((i,-.5)--(i,.5),linewidth(1));
}

for(int i=1; i<6; ++i)
{

draw((i,-.5)--(i,.5),linewidth(1));
}

for(int i=-5; i<0; ++i)
{

draw((-.5,i)--(.5,i),linewidth(1));
}

for(int i=-5; i<0; ++i)
{

draw((-.5,-i)--(.5,-i),linewidth(1));
}

label("$x$", (8,0));
label("$y$", (0,8));

[/asy]

level

Level 2

type

Geometry

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Source and history

task_id
6f508a66-1632-5c52-ab92-79633e602df5
task_key
geometry--test--6f508a66-1632-5c52-ab92-79633e602df5
task_revision_id
1
config / split
geometry / test

Official source

initial import