Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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Which of the following represents a vertical symmetry line for an ellipse centered at (h, k)?

(h, k+b) and (h, k-b)
(h+a, k) and (h-a, k)
(h, k) and (k, h)
(h, 0) and (0, k)

The correct answer is: (h, k+b) and (h, k-b)

For an ellipse centered at the point (h, k), the vertical line of symmetry will run vertically through the center of the ellipse. This means that if you were to draw a vertical line at x = h, it would divide the ellipse into two mirror-image halves. The correct representation of this symmetry can be illustrated by examining the points (h, k+b) and (h, k-b). Here, the coordinates indicate that the vertical line remains fixed at the x-coordinate of h while varying the y-coordinate, effectively creating a line that runs vertically through the center of the ellipse at (h, k). By moving the y-coordinate up by b and down by b, the line of symmetry reflects the vertical nature of the shape. This choice captures the essence of vertical symmetry in an ellipse, where the vertical axis (x = h) serves as the line of symmetry that reflects points evenly on either side of the line.