In the coordinate plane, one of the vertices of a square is the point

I will not draw a picture, I think one can solve it wo...
One point (-3-4), Intersection (3,2) so the distance from the first point -3-3=-6 is the midpoint of the square --> whole side 12, 12*12=144 Answer (D)

In order to solve this question we should know both the distance formula and an alternate formula for the area of a square ( for the sake of saving time). The important inference in this question is that the point where "the diagonals of that square intersect at point (3,2) is the midpoint of the square. If we know what the distance between the vertice of the square and the midpoint is then we can know what the length of a diagonal that connects two vertices in the square. If we know what the length of that diagonal is then we can calculate the area of the square... without even having to solve for the length of the square's side.

Step 1
Apply Distance Formula


Step 2
Multiply the length of the diagonal that connects the vertice and the midpoint by two and enter it into the formula for the area of the square

d1 x d2 / 2 = area of square (this is another that is good to have in our arsenal)

Thus
"D"

VERITAS PREP OFFICIAL SOLUTION:

Because the point of intersection is up and to the right of the given vertex of the square, you can intuit that the given point is the lower, left-hand vertex of the square. Getting from that point (-3, -4) to the center of the square requires going over 6 (from -3 to 3) and up 6 (from -4 to 2). Doing so again, from the center on (3, 2) to the upper right vertex of (9, 8), allows you to fill in the rest of the square. Going from the lower left to the upper right requires going over 12 and up 12, meaning that the square has sides of 12. Accordingly, the area is 144.
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Hi,

I will really appreciate if you can tell me how you came up with the inference that the point at which the diagonal intersect will be the midpoint of the diagonal.
"The important inference in this question is that the point where "the diagonals of that square intersect at the point (3,2) is the midpoint of the square. "

Thanks in advance

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