Question

Use the distance formula to find the distance between point A(-5, 4) and point B(7, -5)

Answer 1

`\boxed{ \bold{ \huge{ \boxed{ \sf{15 \: units}}}}}`

Explanation:

Given,

A( -5 , 4 )⇒ ( x₁ , y₁ )

B ( 7 , -5 )⇒ ( x₂ , y₂ )

Finding distance between these two points

`{ \boxed{ \sf {{ distance = \sqrt{ {(x2 - x1)}^(2) + {(y2 - y1)}^(2)}}}}}`

plug the values

`\sf{ = \sqrt{ {(7 - ( - 5))}^(2) + {( - 5 - 4)}^(2) } }`

`\sf{ = \sqrt{ {(7 + 5)}^(2) + {( - 5 - 4)}^(2) } }`

Calculate the sum

`\sf{ = \sqrt{ {12}^(2) + {( - 9)}^(2) } }`

Evaluate the power

`\sf{ = √(144 + 81) }`

Add the numbers

`\sf{ = √( 225) }`

Calculate

`\sf{ = 15 \: units}`

Hope I helped!

Best regards!!