Question

Determine the distance between the points A and B using Pythagoras
theorem

Answer 1

Distance between the points A and B is 5.

Explanation:

Let's say point C is at coordinates (2;5), therefore distance between the points A and C is 4. Let's call this side a. Distance between points C and B is 3. Let's call this side b.

a²+b² = c²

we need to find hypotenuse c.

c = √4²+3²

c=√16+9

c=√25

c=5

Answer 2

AB = 5 units

Explanation:

From inspection of the graph:

• Point A = (2, 1)
• Point B = (5, 5)

Pythagoras' Theorem: a² + b² = c²

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Create a right triangle by drawing a line from point A to (5, 1), a line from point B to (5, 1), and a line from A to B.

Therefore,

• short leg = 5 - 2 = 3
• long leg = 5 - 1 = 4
• hypotenuse = AB

Using Pythagoras' Theorem:

⇒ 3² + 4² = AB²

⇒ AB² = 25

⇒ AB = √25

⇒ AB = 5