midpoint

Examples of midpoint in the following topics:

• The Distance Formula and Midpoints of Segments

  • The distance and the midpoint formulas give us the tools to find important information about two points.
  • If you have two points, $(x_{1},y_{1})$ and $(x_{2},y_{2})$, the midpoint of the segment connecting the two points can be found with the formula:
  • Another way to interpret this formula is an average: we average the $x$-coordinates to find the $x$-coordinate of the midpoint, and we average the $y$-coordinates to find the $y$-coordinate of the midpoint.
  • The equation for a midpoint of a line segment with endpoints $(x_{1},y_{1})$and $(x_{2},y_{2})$
  • Calculate the midpoint of a line segment and the distance between two points on a plane

• Calculating Elasticities

  • The basic elasticity formula has shortcomings which can be minimized by using the midpoint method or calculating the point elasticity.
  • The midpoint method calculates the arc elasticity, which is the elasticity of one variable with respect to another between two given points on the demand curve .
  • The midpoint method uses the midpoint rather than the initial point for calculating percentage change, so it is symmetric with respect to the two prices and quantities demanded.
  • In contrast to the midpoint method, calculating the point elasticity requires a defined function for the relationship between price and quantity demanded.

• Interpretations of Price Elasticity of Demand

  • Below the midpoint of a straight line demand curve, elasticity is less than one and the firm wants to raise price to increase total revenue.
  • Above the midpoint, elasticity is greater than one and the firm wants to lower price to increase total revenue.
  • At the midpoint, E1, elasticity is equal to one, or unit elastic.

• Linear and Quadratic Functions

  • ., the midpoint of a line segment remains the midpoint after transformation).

• Binary Fission

  • The bacterial chromosome is attached to the plasma membrane at about the midpoint of the cell.
  • After the chromosomes have cleared the midpoint of the elongated cell, cytoplasmic separation begins.

• Meiosis II

  • In prometaphase I, microtubules attach to the fused kinetochores of homologous chromosomes, and the homologous chromosomes are arranged at the midpoint of the cell in metaphase I.
  • In prometaphase II, microtubules attach to the kinetochores of sister chromatids, and the sister chromatids are arranged at the midpoint of the cells in metaphase II.

• Approximate Integration

  • Popular methods use one of the Newton–Cotes formulas (such as midpoint rule or Simpson's rule) or Gaussian quadrature.

• Area and Arc Length in Polar Coordinates

  • For each subinterval $i = 1, 2, \cdots , n$, let $\theta_i$ be the midpoint of the subinterval, and construct a sector with the center at the pole, radius $r(\theta_i)$, central angle $\Delta \theta$ and arc length $r(\theta_i)\Delta\theta$.

• Range

  • The mid-range is the midpoint of the range; as such, it is a measure of central tendency.

• A Graph of Averages

  • The averages of the $y$ values in those intervals are plotted against the midpoints of the intervals.