Question

What is the distance between M(9, −5) and N(−11, 10)?

Answer 1

`\boxed{ \bold{ \huge{ \boxed{ \sf{25 \: units}}}}}`

Explanation:

Let M ( 9 , -5 ) be ( x₁ , y₁ ) and N ( - 11 , 10 ) be ( x₂ , y₂ )

Finding the distance between these points

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

`\longrightarrow{ \sf{ \sqrt{ {( - 11 - 9)}^(2) + {(10 - ( - 5))}^(2) } }}`

`\longrightarrow{ \sf{ \sqrt{ {( - 20)}^(2) + {(10 + 5)}^(2) } }}`

`\longrightarrow{ \sf{ \sqrt{ {( - 20)}^(2) + {(15)}^(2) } }}`

`\longrightarrow{ \sf{ √(400 + 225)}}`

`\longrightarrow{ \sf{ √(625)}}`

`\longrightarrow{ \sf{ \sqrt{ {(25)}^(2) } }}`

`\longrightarrow{ \sf{25 \: units}}`

Hope I helped!

Best regards! :D