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Daily Dose 022 | Mathematics
How can you find the distance between two points?
Being asked to find the distance between two points is one thing, doing it fast, under pressure, is another.
Measuring a line segment between two points in a vertical or horizontal cartesian grid is easy enough.
When distances lay conveniently along the x-axis or y-axis, clearly marked out by the default coordinates along each axis, determining what we need can be done with our eyes closed.
But what about those diagonal distances?
How can we quickly find the distance between two points when it runs at some angle across the coordinate system, or outside the context of a grid altogether and not so nicely inline with an axis?
In this lesson, we dive in to an FE Exam Practice Problem in the subject of MATHEMATICS, specifically learning how to find the distance between two points using the DISTANCE FORMULA.
Key Definition
What is the DISTANCE FORMULA?
In MATHEMATICS, the DISTANCE FORMULA is a variant of the Pythagorean Theorem, used to help us determine the distance between two points.
Given two points, we could always plot them, draw the right triangle, and then find the length of the hypotenuse…but this obviously wouldn’t be a great use of our time when it comes to the FE Exam.
Alternatively, we could put the data we are given straight in to the formula provided to us in the NCEES Reference Handbook.
The Process
What is the process to find the distance between two points?
One fundamental concept you are going to need to know how to deploy on the FE Exam is how to find the distance between two points.
In what context it will be presented is unknown, but what is known, is that it will be needed in some problem along the way.
So let’s discuss using the Distance Formula.
The Distance Formula is like having a mathematical GPS that calculates the shortest path between two points. In engineering, this formula isn’t just about finding numerical distances; it’s used in designing roads, bridges, and even in programming robots to navigate.
It’s a straightforward yet powerful tool that combines algebra and geometry to solve real-world problems.
Let’s run through the process:
- Identify the Coordinates of the Points
- Write Down the Distance Formula
- D = sqrt((x2 – x1)2 + (y2 – y1)2)
- Plug in the Coordinates
- Calculate the Squares
- Add the Squares
- Find the Square Root
- Check Your Answer
Determine the coordinates of the two points you’re measuring. Label them as A(x1, y1) and B(x2, y2).
The distance formula represents the distance (D) between the two points and is written as:
Substitute the x and y coordinates of your points into the formula. Replace x1, y1, x2, and y2 with the respective coordinates.
Compute the square of the differences in x-coordinates and y-coordinates.
Add the squared values together.
Calculate the square root of the sum to find the distance D.
Review your calculations to ensure accuracy in the arithmetic process.
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
