How to find a rectangle on a coordinate plane

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SSAT Middle Level Quantitative › How to find a rectangle on a coordinate plane

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Identify the correct set of coordinates for rectangle $\small ABCD$ .

$\small (-11,3),(-11,7),(3,3),(3,7)$

$\small (-11,3),(11,7),(3,3),(-3,7)$

$\small (11,3),(-10,7),(3,3),(3,7)$

$\small (-11,3),(-11,7),(-3,-3),(3,7)$

Explanation

To identify the correct set of coordinate points for rectangle $\small ABCD$ , note that the correct set must have two sets of matching $\small x$ coordinates and two sets of matching $\small y$ coordinates. The only answer choice that meets these specifications is: $\small \small (-11,3),(-11,7),(3,3),(3,7)$

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In the above figure Dr. Robinson's shed is represented by the red square, and the shed has a perimeter of $\small 12$ yards. Find how much area Dr. Robinson has in his backyard--excluding the area that the shed occupies.

$\small \small 111$ $\small yards^2$

$\small 120$ $\small yards^2$

$\small 129$ $\small yards^2$

$\small 110$ $\small yards^2$

Explanation

To find how much area Dr. Robinson has around his shed in his backyard, first apply the formula: $\small \small P=4S$ , where $\small S$ represents one side of the red shed. Given that $\small \small P=12$
$\small S$ must equal $\small 3$ because $\small 4\times3=12$ .

Now you have enough information to find the area of the red shed.
Apply the formula: $\small A=S^2$
$\small A=3^2=3\times3=9$

Since the rectangular fence has a width of $\small 15$ yards and a length of $\small 8$ yards, apply the formula: $\small Area=width\times length$ in order to find the area of the entire backyard.
Thus,
$\small Area=15\times8=120$

Then simply find the difference between the area of the entire yard and the area of the shed.

Thus the final solution is:
$\small 120-9=111$

Dr. Robinson recently put a rectangular fence around his backyard. The fence has a width of $\small 15$ yards and a length of $\small 8$ yards. If Dr. Robinson paid $\small \small \$ 12.50$ for every yard of fence, how much did the fence cost?