1.
The distance from (1, 0) to (x, 0) is equal to 1. While there is more than one possible x-coordinate for the second point, which of the following options satisfies the distance formula with the given coordinates?
Correct Answer
D. 0
Explanation
The distance between two points in a coordinate plane is given by the distance formula, which is the square root of the difference in x-coordinates squared plus the difference in y-coordinates squared. In this case, the y-coordinates are both 0, so the formula simplifies to the absolute value of the difference in x-coordinates. The distance from (1, 0) to (x, 0) is equal to 1, so the absolute value of the difference in x-coordinates must also be 1. The only option that satisfies this is 0, as the absolute value of the difference between 1 and 0 is 1.
2.
Distance can be negative.
Correct Answer
B. False
Explanation
Distance cannot be negative because it is a scalar quantity that represents the length between two points. It is always a positive value or zero, as it measures the magnitude of displacement. Negative values are not applicable in the context of distance.
3.
The distance from (6,7) to (8,9) is equal to (leave your answer in a simplified radical form - i.e., no decimals)
Correct Answer
A. 2√2 units
Explanation
The distance between two points (x1, y1) and (x2, y2) can be calculated using the distance formula:
d = √((x2 - x1)² + (y2 - y1)²)
In this case, the points are (6, 7) and (8, 9). Applying the distance formula:
d = √((8 - 6)² + (9 - 7)²)
d = √(2² + 2²)
d = √(4 + 4)
d = √8
So, the distance between (6, 7) and (8, 9) is 2√2 units.
4.
The distance from (-1,-2) to (3,4) is equal to (leave your answer in a simplified radical form - i.e., no decimals)
Correct Answer
D. 2√13 units
Explanation
The distance between two points in a coordinate plane can be found using the distance formula, which is the square root of the sum of the squares of the differences in the x-coordinates and the y-coordinates of the two points. In this case, the x-coordinates are -1 and 3, and the y-coordinates are -2 and 4. Using the distance formula, we get the square root of ((3-(-1))^2 + (4-(-2))^2), which simplifies to the square root of (16 + 36), which is the square root of 52. Therefore, the distance is 2√13 units.
5.
Which of the following is an appropriate label for distance?
Correct Answer
B. Kilometers
Explanation
Kilometers is an appropriate label for distance because it is a unit of measurement specifically used to quantify length or distance. It is commonly used in many countries around the world and is a standard unit in the International System of Units (SI). Kilometers are used to measure long distances, such as the distance between cities or the length of a road. It is a suitable label for distance as it accurately represents the concept of measuring how far apart two points are from each other.
6.
Which of the following is NOT an appropriate label for distance?
Correct Answer
A. Joules
Explanation
The label "Joules" is not an appropriate label for distance. Joules is a unit of energy in the International System of Units (SI), not a measure of distance. Meters, feet, and yards, on the other hand, are all units used to measure distance.
7.
The distance from (2,-2) to (5,2) is equal to (leave your answer in a simplified radical form - i.e., no decimals)
Correct Answer
D. 5 units
8.
Which of the following equations represents the distance formula? (Hint: there is more than one correct answer)
Correct Answer(s)
A.
B.
D.
Explanation
The distance formula represents the distance between two points in a coordinate plane. It is calculated using the Pythagorean theorem, where the square of the difference in the x-coordinates is added to the square of the difference in the y-coordinates, and then taking the square root of the sum. The equation that represents the distance formula is d = √((x2 - x1)^2 + (y2 - y1)^2).
9.
The distance from (-1,4) to (4, -1) is equal to (leave your answer in a simplified radical form - i.e., no decimals)
Correct Answer
B. 5√2 units
10.
Find the distance between the two points (4, 1) and (10, 9) (leave your answer in a simplified radical form - i.e., no decimals)
Correct Answer
B. 10 units
Explanation
The distance between two points can be found using the distance formula: √((x2 - x1)^2 + (y2 - y1)^2). In this case, the coordinates of the two points are (4, 1) and (10, 9). Plugging these values into the formula, we get √((10 - 4)^2 + (9 - 1)^2) = √(6^2 + 8^2) = √(36 + 64) = √100 = 10 units.