The Distance Formula

Show your work for each problem.

1.
What is the distance formula used to find?
1. a)The area of a triangle
2. b)The midpoint between two points
3. c)The distance between two points on a coordinate plane
4. d)The slope of a line
Answer: The distance between two points on a coordinate plane
The distance formula calculates the straight-line distance between any two points on a coordinate plane using the Pythagorean theorem.
2.
Find the distance between and .
Answer: 5
. This is the classic 3-4-5 Pythagorean triple.
3.
Find the distance between and .
Answer: 5
4.
Find the distance between and .
Answer: 10
1. What is ? 8
2. What is ? 6
3. What is ? 100
4. What is ? 10
5.
Which theorem is the distance formula based on?
1. a)Binomial theorem
2. b)Pythagorean theorem
3. c)Fundamental theorem of algebra
4. d)Mean value theorem
Answer: Pythagorean theorem
The distance formula is derived from the Pythagorean theorem: . The horizontal and vertical distances are the legs, and the actual distance is the hypotenuse.
6.
Find the distance between and .
Answer: 10
7.
Find the distance between and .
Answer: 10
1. What is ? 8
2. What is ? 6
3. What is ? 100
4. What is the distance? 10
8.
What is the distance between and ?
1. a)
2. b)
3. c)
4. d)
Answer:
. The diagonal of a unit square is .
9.
Find the distance between and .
Answer: 5
1. What is ? 4
2. What is ? -3
3. What is ? 25
4. What is ? 5
10.
Find the distance between and .
Answer: 13
. The 5-12-13 triple is another common Pythagorean triple.
11.
Does the order of the points matter in the distance formula?
1. a)Yes, but only for negative coordinates
2. b)No, because squaring eliminates negative signs
3. c)No, but the answer will be negative if reversed
4. d)Yes, you must always go left to right
Answer: No, because squaring eliminates negative signs
Order does not matter because we square the differences. and both equal 9. Distance is always positive.
12.
Find the distance between and .
Answer: 13
1. What is ? 12
2. What is ? 5
3. What is ? 169
4. What is the distance? 13
13.
Find the distance between and . Give your answer as a whole number or simplified square root.
Answer: 5
14.
A player is at position on a game grid. An enemy is at . If the player's attack range is 13 units, can they attack the enemy?
Answer: Yes
1. What is the horizontal distance ()? 12
2. What is the vertical distance ()? 5
3. What is ? 169
4. What is the distance? 13
5. Can the player attack? (Yes/No) Yes
15.
What is the distance between and ?
1. a)
2. b)
3. c)
4. d)
Answer:
. This cannot be simplified further since 13 is prime.
16.
Find the distance between and .
Answer: 13
1. What is ? 12
2. What is ? 5
3. What is ? 169
4. What is the distance? 13