The distance formula is important for the ACT® Math section. It's an extension of the Pythagorean theorem, which makes it easier to understand and remember.
The Distance Formula
In this formula, (x1, y1) represents the coordinates of the starting point, and (x2, y2) represents the coordinates of the ending point of the line segment.
As you'll see above, the chart of a triangle ABC is used to show the distance of side c. We take the and the , the and . The and are the end of the line segment c. That makes , . Line segment starts at , so both and are 0. That makes the equation look so:
Sqrt
Sqrt
Sqrt
Sqrt
10 = c
Practice Section
Question 1:
Find the distance between the points and .
- A)
- B) 5
- C) 6
- D)
- E) 8
Click for the Answer
Correct Answer: A)
Explanation:
Using the distance formula:
Question 2:
Find the distance between the points and .
- A) 5
- B)
- C) 6
- D) 7
- E)
Click for the Answer
Correct Answer: B)
Explanation:
Using the distance formula:
Question 3:
Find the distance between the points and .
- A) 13
- B)
- C) 10
- D)
- E) 15
Click for the Answer
Correct Answer: A) 13
Explanation:
Using the distance formula:
How will this show up on the ACT Math Test?
I showed you how the distance formula is basically the Pythagorean theorem so you can solve these questions on the ACT Math® section. I find that students have an easier time remembering explicit formulas when they understand the concepts behind them.
They're likely to either ask you for the formula, which you now understand. The test may ask you to use the explicit formula to solve for the distance between two points.
More rarely, they'll ask you to deduce the distance, leaving out certain variables, sometimes from a triangle. In that case, you have to read the question and fill in any given values from the problem. Then, use algebra to find any missing values.
On the ACT® Math test, you'll either need to apply the distance formula directly or use it as part of a more complex problem.