Rectangular Geometry Fundamentals

  1. Which of the points \((2,7)\) or \((-8,1)\) or \((5,3)\) is closest to the origin?
  2. What is the midpoint between \((2,7)\) and \((5,3)?\)
  3. Given a line segment with one endpoint at \((2,7)\) and midpoint at \((-8,1),\) what must the coordinates of the other endpoint be?
  4. Consider the circle with center \((-7,3)\) and radius \(4.\) First sketch this circle, then answer these questions.
    1. What is an equation for the circle?
    2. What are the coordinates of the point(s) where this circle intersects the \(y\)-axis?
    3. What is the area of this circle?
    4. What is the circumference of this circle?
  5. What are the \(x\)-coordinates of the points on the circle \((x-2)^2 + (y+1)^2 = 25\) with \(y\)-coordinate \(3?\)