Question

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

Answer 1

Answer:

$\huge{ \boxed{ \bold{ \tt{2 \sqrt{26}}} \: \: \text{units} } }$

♁ 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 ).

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

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

$\longrightarrow{ \sf{ \sqrt{4 + 100}}}$

Add the numbers : 4 and 100

$\dashrightarrow{ \sf{ \sqrt{104}}}$

$\dashrightarrow{ \boxed{ \sf{2 \sqrt{26} }}}$ units

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

And we're done!

Hope I helped!

Have a wonderful time ! シ

~TheAnimeGirl