1. Lesson 2.7
Core Focus on Geometry
The Distance Formula

2. Warm-Up
Find the perimeter of the triangle formed by the points given below. Round to the nearest tenth when necessary. F(7, 1) G(7, 8) H(3, 1)
≈ 19.1 units

3. Lesson 2.7
The Distance Formula
Find the distance between two points on a coordinate plane using the Distance Formula.

4. Vocabulary
Distance Formula The formula that allows you to find the distance between any two points on a coordinate plane without graphing first. a2 + b2 = c2  (x2 – x1)2 + (y2 – y1)2 = c2 
The vertical leg of the right triangle is the difference between the y-coordinates in the ordered pairs.
The horizontal leg of the right triangle is the difference between the x-coordinates in the ordered pairs.

5. The Distance Formula
The distance, d, between two points (x1, y1) and (x2, y2) is found by:

6. Using the Pythagorean Theorem Using the Distance Formula
Example 1
Find the distance between (1, 2) and (4, 6). The distance between (1, 2) and (4, 6) is 5 units.
Using the Pythagorean Theorem
Using the Distance Formula
= c2
= c2
25 = c2
5 = ca
Let (x1, y1) = (1, 2) and (x2, y2) = (4, 6).

7. Example 2
Find the distance between (0, 8) and (3, 2). Round to the nearest tenth. Write the distance formula. Substitute each value from the ordered pairs into the formula. According to the order of operations, simplify the inside of the parentheses first. Simplify by squaring. Add. Simplify. Round to the nearest tenth. The distance between (3, 2) and (0, 8) is about 6.7 units.

8. Remember that a negative number squared becomes positive.
Example 3
Find the perimeter of ΔMAT to the nearest tenth. Find the length of each side of the triangle using the Distance Formula.
Remember that a negative number squared becomes positive.

9. The perimeter of ΔMAT is approximately 23.3 units.
Example 3 Continued…
Find the perimeter of ΔMAT to the nearest tenth. Find the length of each side of the triangle using the Distance Formula. Add the lengths of the three = 23.3 sides of the triangle.
The perimeter of ΔMAT is approximately 23.3 units.

10. Communication Prompt
When finding the distance between two points, do you prefer using the distance formula or graphing the two points and using the Pythagorean Theorem? Explain your reasoning.

11. Exit Problems
Use the distance formula to find the distance between each pair of points. If necessary, round to the nearest tenth. 1. (2, 7) and (4, 10) 2. (−8, 3) and (7, 11)
≈ 3.6 units
≈ 17 units