Grace S.

asked • 09/13/21

How do I determine the location of a missing point?

1 Expert Answer

By:

Mark M.

The topic is Geometry. What if the missing point is the end-point? mid-point?
Report

09/14/21

Greg H.

tutor
The answer is the same for algebra, geometry, and calculus. If you know the function that specifies the coordinates of an object in 2 or 3 (or n) dimensions, you can determine the location of any missing point. Determining the midpoint and endpoints is simple for simple geometric functions, but may result in zero or more than one midpoint or more than one endpoint for more complex functions, e.g. circle or sphere. If you don't know or can't determine the function to do the mapping, you can use interpolation. There are any number of analytical and computational techniques to interpolate in any number of dimensions.
Report

09/14/21

Greg H.

tutor
Linear interpolation is a simple way to infer the location of a missing data point. For linear interpolation, you assume that points lie along a straight line. For example, if you have two data points at (4,4) and (6.8), you can assume that a straight line connects the two. You can determine the slope of the line segment with m = (y2-y1) / (x2-x1), and determine the y-intercept by substituting one of the data points in the standard equation for a line: slope = (8-4) / (6-4) = 4/2 = 2 Standard form equation: y=mx+b: y=2x+b Determine b: Substitute one of the data points in the standard form: y=mx+b: 8=2(6)+b, 8=12 + b, b=-4 The equation of the inferred line is y=2x-4. Then if you want to find the location of the missing point at x=5, just substitute in the equation: y=2x-4; y=2(5) -4; y=10-4; y=6. Linear interpolation is simple and works well, but the assumption that the points lie along a straight line is often wrong. For example, think of a rocket ship or a bullet: it will travel a very short distance in the first few seconds but will accelerate to supersonic velocities very quickly.
Report

09/14/21

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.