Answer:
[tex] \huge{ \boxed{ \bold{ \tt{2 \sqrt{26}}} \: \: \text{units} } } [/tex]
♁ Question :
- Find the distance between ( 5 , -6 ) and ( 3 ,4 ).
♁ 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 ).
[tex] \boxed{ \underline{ \sf{distance = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } }}}[/tex]
Substitute the actual value of the points into the distance formula and then simplify.
[tex] \dashrightarrow{ \sf{ \sqrt{ {(3 - 5)}^{2} + {(4 - ( - 6))}^{2} } }}[/tex]
Remember : The positive and negative integer are always subtracted but posses the sign of the bigger integer.
[tex] \dashrightarrow{ \sf{ \sqrt{ {( - 2)}^{2} + {(4 - ( - 6))}^{2} } }}[/tex]
Remember : ( - ) × ( - ) = ( + )
[tex] \dashrightarrow{ \sf{ \sqrt{ {( - 2)}^{2} + {(4 + 6)}^{2} } }}[/tex]
Add the numbers : 4 and 6
[tex] \longrightarrow{ \sf{ \sqrt{ {( - 2)}^{2} + {(10)}^{2} } }}[/tex]
Evaluate the power
[tex] \longrightarrow{ \sf{ \sqrt{4 + 100}}} [/tex]
Add the numbers : 4 and 100
[tex] \dashrightarrow{ \sf{ \sqrt{104}}} [/tex]
[tex] \dashrightarrow{ \boxed{ \sf{2 \sqrt{26} }}}[/tex] units
Therefore , The distance between ( 5 , -6 ) and ( 3 , 4 ) is [tex] \sf{2 \sqrt{26}} [/tex] units .
And we're done!
Hope I helped!
Have a wonderful time ! シ
~TheAnimeGirl
