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Coordinate Geometry Formulas You Must Know for the ACT

Some of the questions on the ACT Math test deal with coordinate geometry. When solving coordinate geometry problems, there are several useful formulas you should remember:

  • Midpoint formula. The formula for coordinates of the midpoint of a line segment between any two points (x1, y1) and (x2, y2) is:

    image0.png
  • Distance formula. The formula for the length of a line segment between any two points (x1, y1) and (x2, y2) is:

    image1.png
  • Rise-run slope formula. The formula for the slope of a line in terms of the rise and the run is:

    image2.png
  • Two-point slope formula. The formula for the slope of a line that includes the points (x1, y1) and (x2, y2) is:

    image3.png
  • Axis of symmetry of a parabola. The axis of symmetry is the vertical line that divides a parabola down the middle. For a quadratic function y = ax2 + bx + c, the formula for the equation of the axis of symmetry is:

    image4.png
  • Vertex of a parabola. The vertex of a parabola is the point where the parabola changes directions. It’s always either the lowest or the highest point on the parabola. Here’s the formula for the coordinates of the vertex for the quadratic function y = ax2 + bx + c:

    image5.png
  • Formula for graphing a circle. The formula for the equation of a circle of radius r centered at the point (h, k) is:

    (xh)2 + (yk)2 = r2

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