Question

Valerie's work deriving the distance formula for length d is shown.

Evaluate her work and explain any errors.

the drop down answers are

does form/does not form
correctly/incorrectly
should not square distance terms/should subtract not add the distance terms/should square d/correctly wrote all terms

Answer 1

Step-by-step explanation:

hope you can understand

Answer 2

As per the conditions for evaluating distance,

a. She chose a point that does form a right angle.

b. She correctly wrote the length of each of the legs which is equals to $(x_{2} -x_{1} )$ and $(y_{2} -y_{1} )$ .

c. She should square d in the equation.

What is distance?

" Distance is defined as one dimensional which represents the total length between two endpoints."

According to the question,

As per the graph,

In a right triangle we have,

Two coordinates at distance $'d'$

$( x_{1}, y_{1} ) \\\\( x_{2}, y_{2} )$

a. Right angle formed at a point $(x_{2} ,y_{1} )$.

She chose a point that does form a right angle.

b. Length of each leg

Along y- axis $= (y_{2} -y_{1} )$

Along x- axis $= (x_{2} -x_{1} )$

She correctly wrote the length of each of the legs which is equals to $(x_{2} -x_{1} )$ and $(y_{2} -y_{1} )$ .

c. Distance $'d'$ formula between  $( x_{1}, y_{1} ) ,( x_{2}, y_{2} )$ is equals to

   

   $d^{2} = = (x_{2} -x_{1} )^{2} + = (y_{2} -y_{1} )^{2}$

She should square d in the equation.

Hence, As per the conditions for evaluating distance,

a. She chose a point that does form a right angle.

b. She correctly wrote the length of each of the legs which is equals to $(x_{2} -x_{1} )$ and $(y_{2} -y_{1} )$ .

c. She should square d in the equation.

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