Question

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

Answer 1

Answer

$\boxed{10 \: \: units}$

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

$\mathsf{ \sqrt{64 + 36} }$

Add the numbers

$\mathsf{ \sqrt{100} }$

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!