Question

Recall that the absolute value $|a|$ of a number is its distance from zero. For example, $|-3| = 3$ and $|9-7| = |7-9| = 2$.

Enter the letters of the points that are on the graph of $|x| = |y|$.

[asy]
unitsize(0.4 cm);

pair A, B, C, D, E, F, G, H, I, J;

int i;

A = (3,3);
B = (-5,-4);
C = (-4,1);
D = (6,-1);
E = (6,6);
F = (-2,-2);
G = (-3,5);
H = (6,-6);
I = (2,4);
J = (2,-3);

for (i = -8; i <= 8; ++i) {
draw((i,-8)--(i,8),gray(0.7));
draw((-8,i)--(8,i),gray(0.7));
}

draw((-8,0)--(8,0),linewidth(1.5*bp),Arrows(6));
draw((0,-8)--(0,8),linewidth(1.5*bp),Arrows(6));

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

dot("$A$", A, SE);
dot("$B$", B, S);
dot("$C$", C, NW);
dot("$D$", D, SE);
dot("$E$", E, SE);
dot("$F$", F, SE);
dot("$G$", G, NW);
dot("$H$", H, SE);
dot("$I$", I, NW);
dot("$J$", J, NE);
[/asy]

Type your answer as a list, separated by commas. For example, if you think points $B,$ $D,$ and $G$ lie on the graph, then enter "B, D, G".

Answer 1

The points that are on the graph of |x| = |y| are A, E, F, and H.

How to determine the points on the graph of the equation

From the question, we have the following parameters that can be used in our computation:

A = (3,3); B = (-5,-4); C = (-4,1); D = (6,-1); E = (6,6); F = (-2,-2); G = (-3,5); H = (6,-6); I = (2,4); J = (2,-3);

To find the points on the graph of the equation |x| = |y|, we need to identify the points where the absolute value of the x-coordinate is equal to the absolute value of the y-coordinate.

Checking each of the given point, we have

• A = (3,3): The absolute value of 3 is equal to the absolute value of 3. Yes.
• B = (-5,-4): The absolute value of -5 is not equal to the absolute value of -4. No.
• C = (-4,1): The absolute value of -4 is not equal to the absolute value of 1. No.
• D = (6,-1): The absolute value of 6 is not equal to the absolute value of -1. No.
• E = (6,6): The absolute value of 6 is equal to the absolute value of 6. Yes.
• F = (-2,-2): The absolute value of -2 is equal to the absolute value of -2. Yes.
• G = (-3,5): The absolute value of -3 is not equal to the absolute value of 5. No.
• H = (6,-6): The absolute value of 6 is equal to the absolute value of -6. Yes.
• I = (2,4): The absolute value of 2 is not equal to the absolute value of 4. No.
• J = (2,-3): The absolute value of 2 is not equal to the absolute value of -3. No.

Hence, the points on the graph of |x| = |y| are A, E, F, and H.