So unfortunately I can't draw on this thing. You can plot the points according to the (x, y) ordered pairs. The first number in each pair is how many units you move along the x axis (horizontal) and the second number is how many units to move along the y axis (vertical or up and down). For (-5, -2) start at the center (where the lines cross) and go backwards 5 spaces. Staying on that -5 line, go down 2 spaces. That's where you will put your first point. For (-5, 9) go backwards 5 spaces, but this time go up 9 spaces. This is the location for your second point. (9, 9) requires you to go forward 9 spaces, and up 9 spaces. And finally for (9,-2) go forward 9 space[tex]d = \sqrt{(x_{2}-x_{1} )^{2} - (y_{2}-y_{1} )^{2}}[/tex]s, and down 2. When you connect the dots, you should get a rectangle.
Now find the perimeter of the rectangle by counting the squares. Multiply what you get by 10 to get the number of meters. That is the graphical way to solve.
You could also use the distance formula:
[tex]d = \sqrt{(x_{2}-x_{1} )^{2} - (y_{2}-y_{1} )^{2}}[/tex]
Since either y or x will be the same for each pair, a significant portion of this formula can be ignored. For the first pair, let's do (-5, 9) and (9, 9). This would be the top of the rectangle.
Put this into the formula and get:
[tex]d = \sqrt{(9-(-5) )^{2} - (9-9 )^{2}}\\\\= \sqrt{(14 )^{2} - 0}\\\\=\sqrt{14^{2}}}\\\\= 14[/tex]
So the first side or length is 14 units.
Now let's do (-5, -2) and (9, -2). The y is the same here so we can just do:
[tex]d = \sqrt{ (x_{2} -x_{1}) - (y_{2}-y_{1} ) ^{2} }\\\\= \sqrt{ (9 -(-5))^{2} - ((-2)-(-2)) ^{2} }}\\\\=\sqrt{13^{2} - 0}\\\\= 13[/tex]
The other side or width is 13 units.
The formula for the perimeter is 2L + 2W.
2(14) + 2(13) = 26 + 28 = 54 units
Now we know that each unit is 10 meters long, so multiply 54 by 10.
The answer is 540 meters.
