Question

The grid shows the positions, in miles, of a subway stop and a house. The image is of a 2-dimensional graph with an x-axis and a y-axis. A point is marked as house with co-ordinate (4,3). Another point with co-ordinate (-4,-3) is marked as subway. To the nearest mile, what is the distance between the subway stop and the house?

Answer 1

Here we can use the distance formula. We label one point $( x_{1}, y_{1})$ and the other $( x_{2}, y_{2})$. It doesn’t matter which point we label with the 1s and which we label with the 2s. The distance will be the same either way (the distance from the subway to the house is the same as that from the house to the subway — to give a related easier to follow example). What does matter is that the 1s are together and the 2s are together.

So let’s call (-4,-3) $( x_{1}, y^{1})$ which means that -4 is $x_{1}$ and -3 is $y_{1}$. We call the other point (4,3) $( x_{2},y_{2})$

The distance formula is $d= \sqrt{( x_{2} - x_{1} )^{2} +( y_{2}-y_{1})^2 }$

We substitute using the points given and obtain:
$d= \sqrt{(3- - 3) ^{2} +( 4- -4)^2 }$

and simplify to get $\sqrt{16+9}= \sqrt{25}=5$

The distance is 5 miles

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