Maya plots the yards lost during a football game on a number line and labels it A. She plots Point B to the right of zero, a distance that is exactly as far from zero as Point A is. Which sentence is a correct statement about Point B?

Question

The sum of the values of Point A and Point B is negative.
The sum of the values of Point A and Point B is zero.
Point B lies twice the distance from 0 as Point A.
Point B lies to the left of Point A on a number line

Answer 1

Let's analyze the situation:

1. Point A is a negative value (since it represents yards lost), meaning it is located to the left of zero on the number line.
2. Point B is a positive value and is plotted to the right of zero, at the same distance from zero as Point A.

Since Point B is the same distance from zero as Point A, if we represent Point A's value as \( -x \) (where \( x \) is a positive number), Point B will be at \( x \).

Now, we can examine each of the given statements:

1. The sum of the values of Point A and Point B is negative.

   • This is false: \( -x + x = 0\).

2. The sum of the values of Point A and Point B is zero.

   • This is true: \( -x + x = 0\).

3. Point B lies twice the distance from 0 as Point A.

   • This is false: Both points are the same distance from zero.

4. Point B lies to the left of Point A on a number line.

   • This is false: Point B lies to the right of zero and thus to the right of Point A.

The correct statement about Point B is: The sum of the values of Point A and Point B is zero.