Question

The distance of the line segment is 36.True or False

Answer 1

Answer: False

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Step-by-step explanation:

If you prefer the pythagorean theorem, then follow the method mentioned by the other response.

I'll use the distance formula as a slight alternative. In fact, the distance formula is a modified version of the pythagorean theorem.

`A = (x_1,y_1) = (-5,5) \text{ and } B = (x_2, y_2) = (3,-1)\\\\d = √((x_1 - x_2)^2 + (y_1 - y_2)^2)\\\\d = √((-5-3)^2 + (5-(-1))^2)\\\\d = √((-5-3)^2 + (5+1)^2)\\\\d = √((-8)^2 + (6)^2)\\\\d = √(64 + 36)\\\\d = √(100)\\\\d = 10\\\\`

The result of the distance formula calculation shows the distance from A(-5,5) to B(3,-1) is exactly 10 units.

This means segment AB is exactly 10 units long.

Therefore, the statement "the line segment is 36 units long" is false

Answer 2

Apply the pythagorean theorem:

c^2 = a^2 + b^2

Where:

c = hypotenuse

a & b = the other 2 sides of the triangle

Replacing:

x^2 = 6^2 + 8^2

x^2 = 36 + 64

x^2 = 100

x= √100

x= 10

Answer: FALSE