Main Idea and New Vocabulary

Example 1: Find Distance on the Coordinate Plane

Example 2: Real-World Example

Key Concept: Distance Formula

Example 3: The Distance Formula

Example 4: The Distance Formula

• Find the distance between two points on the coordinate plane.

• Distance Formula

Find Distance on the Coordinate Plane

Graph the ordered pairs (0, –6) and (5, –1). Then find the distance between the points.

Find Distance on the Coordinate Plane

Answer: The points are about 7.1 units apart.

a2 + b2 = c2 Pythagorean Theorem

52 + 52 = c2 Replace a with 5 and b with 5.

50 = c2 52 + 52 = 25 + 25 or 50

Definition of square root

±7.1 ≈ c Use a calculator.

A. 7.1

B. 7.8

C. 8.1

D. 8.6

Graph the ordered pairs (4, 5) and (–3, 0). Then find the distance between the points.

CITY MAPS Reed lives in Seattle, Washington. One unit on this map is 0.08 mile. Find the approximate distance he drives between Broad Street at Denny Way (–1, 0) and Broad Street at Dexter Avenue North (4, 5).

Let c represent the distance between Denny Way and Dexter Ave along Broad Street. Then a = 5 and b = 5.

a2 + b2 = c2 Pythagorean Theorem

52 + 52 = c2 Replace a with 5 and b with 5.

50 = c2 52 + 52 = 25 + 25 or 50

Definition of square root

±7.1 ≈ c Use a calculator.

Answer: Since each map unit equals 0.08 mile, the distance that he drives is 7.1 • 0.08 or about 0.57 mile.

A. 0.76 mile

B. 0.8 mile

C. 1.13 miles

D. 14.1 miles

CITY MAPS One unit on the map is 0.08 mile. Find the approximate distance along Broad Street between the points at (–4, –3) and (6, 7).

The Distance Formula

Use the Distance Formula to find the distance between points C(4, 8) and D(–1, 3). Round to the nearest tenth if necessary.

Answer: So, the distance between points C and D

is about 7.1 units.

The Distance Formula

Distance Formula

(x1, y1) = (4, 8), (x2, y2) = (–1, 3)

Simplify.

Evaluate (–5)2.

Add 25 and 25.

Use a calculator.

The Distance Formula

a2 + b2 = c2 Pythagorean Theorem

52 + 52 = c2 Replace a with 5 and b with 5.

50 = c2 52 + 52 = 25 + 25 or 50

c Definition of square root

CheckUse the Pythagorean Theorem.

±7.1 ≈ c 7.1 = 7.1 The answer is correct.

A. 2.2 units

B. 3.9 units

C. 8.1 units

D. 13.2 units

Use the Distance Formula to find the distance between the points R(0, –6) and S(–2, 7). Round to the nearest tenth if necessary.

Use the Distance Formula to find the distance between the points G(–3, –2) and H(–6, 5). Round to the nearest tenth if necessary.

The Distance Formula

The Distance Formula

Answer: So, the distance between points G and H is about 7.6 units.

Distance Formula

(x1, y1) = (–3, –2),

(x2, y2) = (–6, 5)

Simplify.

Evaluate (–3)2 and (7)2.

Add 9 and 49.

Use a calculator.

A. 6 units

B. 6.3 units

C. 10 units

D. 10.2 units

Use the Distance Formula to find the distance between the points J(–8, –1) and K(2, 1). Round to the nearest tenth if necessary.