Final answer:
The slope of side AD in square ABCD, with given coordinates for points A and B, is -1/2. This is determined using the concept of negative reciprocal slopes in perpendicular lines.
Step-by-step explanation:
In square ABCD, if points A and B have coordinates (3, 5) and (7, 13) respectively, the slope of line segment AB (side AB) can be found using the slope formula m = (y2 - y1)/(x2 - x1). Hence, m = (13 - 5)/(7 - 3) = 2. Now, as ABCD is a square, sides AD and BC are parallel and have the same slope. Plus, sides AB and BC are perpendicular to AD, and in the plane, if two lines are perpendicular, the slope of one line is the negative reciprocal of the other. So, the slope of side AD would be the negative reciprocal of 2, which is -1/2.
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