akshatgupta87 wrote:Q.) A certain square is to be drawn on a coordinate plane. One of the vertices must be on the origin, and the square is to have an area of 100. If all coordinates of the vertices must be integers, how many different ways can this square be drawn?
A)4
B)6
C)8
D)10
E)12
Step 1: If area = 100, side = 10.
Step 2: Recognize that the hypotenuse of a 6-8-10 triangle is 10.
Step 3: Plot coordinate pairs using every possible combination of (±6,±8), (±8,±6),(0,±10) and (±10,0).
Step 4: Using the plotted points, draw connected squares centered about the origin. Three sets of connected squares are possible:
Number of possible squares = 12.
The correct answer is
E.
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