Correct Answer
Options A coordinates negative 4, 2, \( (-4,2), \) B coordinates 1, negative 3, \( (1,-3), \) and E coordinates 6, 2 \( (6,2) \) should be selected.
Explanation
The square has a perimeter of 20, so the lengths of the sides must add up to 20. Since all four sides of a square have the same length, we need to find the points that are 20 divided by 4 equals 5 \( 20 \div 5 = 4 \) units away from point K.
Point K is located at the coordinates 1, 2, \( (1, 2), \) amd option A is located at the coordinates negative 4, 2. \( (-4,2). \) Both points have a y-coordinate of 2, which means the points are horizontally aligned on the coordinate plane because they lie on the same horizontal line (y equals 2). \( (y = 2). \) Since the y-coordinates are the same, the distance between these points is just the difference in their x-coordinates. The x-coordinates are 1 and negative 4. \( -4. \) The distance between them is the difference between 1 and negative 4. \( -4. \) Distance equals the absolute value of 1 minus open parenthesis negative 4 close parenthesis, which equals the absolute value of 1 plus 4, which equals the absolute value of 5, which equals 5.
$$ \text{Distance} = |1 - (-4)| = |1 + 4| = |5| = 5. $$
Option B, located at the coordinates 1, negative 3, \( (1, -3), \) is vertically aligned with point K. It is also 5 units away from point K, finding the difference in just the y-coordinates. Option E, located at the coordinates 6, 2, \( (6, 2), \) is horizontally aligned with point K. It is also 5 units away from point K, finding the difference in just the x-coordinates.
To complete the explanation, option C is 4 units above point K, and option D is 3 units to the right of point K. Neither one of these should be selected.