Question

What is the distance between the points (5,1) and (-3,-5)?
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Answer 1

`\boxed{10 \: \: units}`

Step by step explanation

Let the points be A and B

A ( 5 , 1 ) ⇒ ( x₁ , y₁ )

B ( -3 , -5 )⇒ ( x₂ , y₂ )

Now, let's find the distance between theses two points:

Distance =
`\mathsf{ \sqrt{ {(x2 - x1)}^(2) + {(y2 - y1)}^(2) } }`

Plug the values

`\mathsf{ \sqrt{ {( - 3 - 5)}^(2) + {( - 5 - 1)}^(2) } }`

Calculate

`\mathsf{ \sqrt{ { ( - 8)}^(2) + {( - 6)}^(2) } }`

Evaluate the power

`\mathsf{ √(64 + 36) }`

Add the numbers

`\mathsf{ √(100) }`

Write the number in exponential form with a base of 10

`\mathsf {\sqrt{ {10}^(2) } }`

Reduce the index of the radical and exponent with 2

`\mathsf{10 \: units}`

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The distance formula is used to determine the distance ( d ) between two points. If the co-ordinates of the two points are ( x₁ , y₁) and ( x₂ , y₂ ) , the distance equals the square root of x₂ - x₁ squared + y₂ - y₁ squared.

Hope I helped!

Best regards!