How to find the distance between points fast?

Daily Dose 033 | Mathematics

How to find the distance between points fast?

Measuring the distance between points should be easy – until it isn’t.

Fortunately, the NCEES Reference Handbook provides us with a formula to plug and play the data when in need.

But what should you do when the distances get a bit more complex in nature?

When the distances are no longer running conveniently along the x-axis or y-axis?

Welp, you can do it manually, but…

At Prepineer, we’ve seen “running out of time” be THE THING that has been the root of most failed FE attempts, so…

Save a ton of time and hack it.

In this lesson, we dive into a FE Exam Practice Problem in the subject of MATHEMATICS, specifically learning how to determine the distance between points fast.

Specifically, we will be showing you how to use your NCEES Approved Calculator to cut the time to solve three-fold.

Key Definition

What is a NCEES APPROVED CALCULATOR?

If it’s your first time hearing this, then I am sorry, but you won’t be able to take in or use any calculators that are not on the NCEES APPROVED LIST for the FE Exam.

That’s right, if you were planning on leaning on your trustworthy TI-89 or CASIO FX-CG10 then you are *ish out of luck.

But don’t worry, we’ve got you dialed in helping you learn how to hack problems using those calculators that are approved by the NCEES.

So if you are wondering…

How to find the distance between points faster…

Then watch this video and learn while others lose precious time doing it manually.

The Process

What is the process to find the distance between points

Let’s talk the distance formula, but more importantly how to find the distance between points faster on your upcoming FE Exam.

Using the distance formula is easy enough when we are given two points fully defined, but what happens when we are given a distance along with partial information on the points?

In this case, we can still use the Distance formula, as it’s presented to us in the NCEES FE Reference Handbook, but it’s going to require much more input, time wise.

So what are we to do?

Hack it using either your TI-36x PRO or Casio FX115ES PLUS, here are the steps:

Using the TI-36X Pro:

1. Access the Equation Solver: Press MODE and navigate to EQN mode, then select NUM-SOL, which stands for Numerical Solver.
2. Enter the Distance Formula: You will be presented with a screen displaying an empty equation.Manually enter the distance formula, adjusting it to solve for the unknown (either x₂ or y₂).

   Recall that the distance formula in general form is written as:

   • d = √((x₂ – x₁)² + (y₂ – y₁)²).

   Fill in known values for d, x₁, y₁, and either x₂ or y₂, depending on which coordinate is unknown and press ENTER

3. Enter a Guess for the Unknown: The calculator will prompt you to enter a guess for the unknown value.Input a reasonable guess based on the context of your problem. This guess helps the calculator start the iteration process.
4. Solve for the Unknown: After entering your guess, the calculator will use iterative methods to solve for the unknown coordinate.
5. Review the Solution: The calculator displays the solved value of the unknown coordinate.Take a look over the answer options and select the appropriate answer.

Using the Casio FX-115ES Plus:

1. Enter Data into Regular Calculation Mode: Unlike the TI-36X Pro, the Casio FX-115ES Plus does not have a dedicated NUM-SLV mode. Instead, input the distance formula directly in the calculation mode. Make sure to set the equation with one variable as the unknown.
2. Use the Solve Function: After entering the formula, press SHIFT, followed by CALC (which accesses the SOLVE function). The calculator will then prompt you for a guess.
3. Input a Guess for the Unknown: Input your guess for the unknown variable (y₂ or x₂). This initial guess will be used by the calculator as a starting point for finding the solution.
4. Calculate and Iterate: The calculator will use your guess to start the iteration process and find the unknown value that satisfies the given conditions.
5. Review the Solution: Once the calculation is complete, the calculator will display the solution, i.e., the value of the unknown coordinate.

Some Distance Formula type problems can certainly present themselves as more difficult than they are because of how you are being presented the data within the problem statement.

However, following the step by step process for whichever calculator you will be using will ensure that you are able to find the distance between points fast, no matter how hard they initially appear.

And with all of that being stated, check out the video and see how we can go about solving this type of problem in the most efficient manner.

As always, we are here to help, Prepineer

Video Review

[VIDEO] How to find the distance between points fast