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2. The east-west streets and north-south avenues of a certain city are numbered consecutively from south to north and west to east. All blocks are squares with the same side lengths. Mandy is standing on the corner of 59th Street and 15thAvenue. Mark is standing on the comer of 35th Street and 21st Avenue. Mark calls Mandy and asks her to meet him at a spot halfway between their currentlocationsb. If Mark stays where he is and Mandy walks to him, how far must she walk?

Respuesta :

Given:

Mark is standing at 35th street and 21st avenue so the coordinates of his position can be taken as (35,21)

Mandy is standing at 59th street and 15th avenue so the coordinates of her position can b taken as (59,15).

Now, if Mark stays where he is and Mandy walks to him,then we have to find the distance she needs to travel.

To find this, we can use distance formula:

Let the two points be:

[tex](x_1,y_1)and(x_2,y_2)[/tex]

Then the distance between them is given by:

[tex]D=\sqrt[]{(x_2-x_{1^{}})^2+(y_2-y_1)^2}[/tex]

According to our question,we have:

[tex](x_1,y_1)=(35,21)and(x_2,y_2)=(59,15)[/tex]

Now, applying distance formula,

[tex]\begin{gathered} D=\sqrt[]{(59-35)^2+(21-15)^2} \\ =\sqrt[]{24^2+6^2} \\ =\sqrt[]{576+36} \\ =\sqrt[]{612} \end{gathered}[/tex][tex]D=24.73[/tex]

Thus, Mandy has to walk 24.73 towards Mark.

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