Question

What is the distance between the following coordinates? Show work.

(5, -6) and (3, 4)
SHOW WORK

Answer 1

`\huge{ \boxed{ \bold{ \tt{2 √(26)}} \: \: \text{units} } }`

♁ Question :

• Find the distance between ( 5 , -6 ) and ( 3 ,4 ).

♁ Step by step Step-by-step explanation:

Let the points be A and B. Now,

• Let, A ( 5 , -6 ) ⇢ ( x₁ , y₁ )
• Let, B ( 3 , 4 ) ⇢ ( x₂ , y₂ )

Use the distance formula to determine the distance between A ( 5 , -6 ) and B ( 3 , 4 ).

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

Substitute the actual value of the points into the distance formula and then simplify.

`\dashrightarrow{ \sf{ \sqrt{ {(3 - 5)}^(2) + {(4 - ( - 6))}^(2) } }}`

Remember : The positive and negative integer are always subtracted but posses the sign of the bigger integer.

`\dashrightarrow{ \sf{ \sqrt{ {( - 2)}^(2) + {(4 - ( - 6))}^(2) } }}`

Remember : ( - ) × ( - ) = ( + )

`\dashrightarrow{ \sf{ \sqrt{ {( - 2)}^(2) + {(4 + 6)}^(2) } }}`

Add the numbers : 4 and 6

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

Evaluate the power

`\longrightarrow{ \sf{ √(4 + 100)}}`

Add the numbers : 4 and 100

`\dashrightarrow{ \sf{ √(104)}}`

`\dashrightarrow{ \boxed{ \sf{2 √(26) }}}` units

Therefore , The distance between ( 5 , -6 ) and ( 3 , 4 ) is
`\sf{2 √(26)}` units .

And we're done!

Hope I helped!

Have a wonderful time ! シ

~TheAnimeGirl