Grades 11-12 Video Solutions 2022-2022_11-12

Video Transcription

Video Summary

To determine how many points on the perimeter of a circle with center (0,0) and radius 5 have integer coordinates, we use the equation \(x^2 + y^2 = 25\). Testing integer values:<br /><br />- \(x = 5\), \(y = 0\)<br />- \(x = 4\), \(y = 3\)<br />- \(x = 3\), \(y = 4\)<br /><br />Only these combinations satisfy the equation. Points where \(x = 2\) or \(x = 1\) do not work since they result in y-values that aren't integers. By leveraging symmetry and rotating these initial points through 90 degrees, each combination appears four times around the circle, totaling 12 points with integer coordinates.

Keywords

circle

integer coordinates

symmetry

perimeter

points