Learning Target: I Can Use the Distance Formula to Determine the Length of Segments

Name ______Module 4

Distance Formula

Learning Target: I can use the distance formula to determine the length of segments.

Opening Exercise

Find the length of the hypotenuse of the right triangle below.

Distance Formula

Using the Pythagorean theorem to find the distance between two points can be summarized using the distance formula.

d=(y2-y1)2+(x2-x1)2

Example 1

Line segment AB has endpoints A(2, -3) and B(-4,6). What is the length of AB to the nearest tenth?

Example 2

Triangle ABC has coordinates A(-6,2), B(-3,6), and C(5, 0). Find the perimeter of the triangle. Express your answer in simplest radical form.

Name ______Module 4

Distance Formula Problem Set

1. What is the distance between the points (-3,2) and (1,0) in simplest radical form?

2. Use the coordinates labeled below to determine the length of the radius of circle C to the nearest tenth of a unit.

3. What is the length, to the nearest tenth, of the line segment joining the points (-4,2) and

(146, 52)?

4. Jerry and Jean Jogger start at the same time from point A shown on the accompanying set of axes. Jerry jogs at a rate of 5 miles per hour traveling from point A to point R to point S and then to point C. Jean jogs directly from point A to point C on AC at the rate of 3 miles per hour. Which jogger reaches point C first? Explain or show your reasoning.

5. Given parallelogram RSTU with vertices R1, 3, S-2,-1,T4,0, and U(7,4). Find the perimeter of the parallelogram; round to the nearest hundredth.

Name ______Module 4

Distance Formula Exit Ticket

1. In circle O, a diameter has endpoints (-5,4) and 3,-6. What is the length of the diameter in simplest radical form?

2. Given triangle ABC with vertices A(6,0), B(-2,2), and C(-3,-2). Find the perimeter of the triangle; round to the nearest hundredth.