how to find the length of a segment

Download Commodity

Download Article

You can measure the length of a vertical or horizontal line on a coordinate plane by simply counting coordinates; however, measuring the length of a diagonal line is trickier. You can use the Distance Formula to detect the length of such a line. This formula is basically the Pythagorean Theorem, which you can come across if you imagine the given line segment as the hypotenuse of a correct triangle.^[one] By using a bones geometric formula, measuring lines on a coordinate path becomes a relatively easy task.

1. one

   Prepare the Distance Formula. The formula states that ${\displaystyle d={\sqrt {(x_{2}-x_{i})^{2}+(y_{2}-y_{i})^{2}}}}$ , where ${\displaystyle d}$ equals the altitude of the line, ${\displaystyle (x_{ane},y_{one})}$ equal the coordinates of the offset endpoint of the line segment, and ${\displaystyle (x_{two},y_{ii})}$ equal the coordinates of the 2d endpoint of the line segment.^[ii]

2. 2

   Observe the coordinates of the line segment'southward endpoints. These might already be given. If not, count forth the x-axis and y-axis to find the coordinates.^[3]

   Advertisement

3. 3

   Plug the coordinates into the Distance Formula. Be careful to substitute the values for the right variables. The two ${\displaystyle ten}$ coordinates should be inside the showtime gear up of parentheses, and the two ${\displaystyle y}$ coordinates should be inside the second set of parentheses.^[4]

   Ad

1. 1

   Summate the subtraction in parentheses. Past using the lodge of operations, whatever calculations in parentheses must be completed outset.^[5]

2. ii

   Square the value in parentheses. The guild of operations states that exponents should be addressed next.^[6]

3. 3

   Add together the numbers under the radical sign. You practise this calculation as if you were working with whole numbers.

4. iv

   Solve for $$ d {\displaystyle d} . To reach your concluding answer, find the square root of the sum under the radical sign.

   Advertisement

Add New Question

• Question

  What exercise we phone call points that are on aforementioned line?

  

  Points on the same direct line are said to be "collinear" or "colinear."

• Question

  How do I simplify the square root?

  

  Wait for a perfect square inside the radical sign, find its square root, and put that square root out in front of the radical sign, indicating that information technology's to be multiplied by the radical. For example: √50 = √(ii x 25) = five√2.

• Question

  The rising is four inches. The angle is 90 degrees from the meridian to the base. What is the slope?

  

  To notice the gradient, you have to know the horizontal distance over which the ascent occurs. The ninety° angle is non relevant.

• Question

  How exercise I detect the altitude of a line if I don't know the end points?

  

  Assuming y'all don't have a measuring tool (tape measure, ruler, etc.), you cannot use the distance formula outlined above without knowing the finish points. However, if the line is given as office of a geometrical figure, there are various geometrical and trigonometrical methods to find the length (too numerous and complicated to care for here).

• Question

  How would I find the length of each segment?

  

  For a line segment, you lot should create a right triangle by making two more than lines. If this line segment is on a dot filigree, every line betwixt two dots is one unit. If the line segment is on a coordinate plane, then you tin do the same or use the altitude formula for a line.

• Question

  A square tabular array has an expanse of 16 sq cm. How do I observe the length of its side?

  

  √sixteen = 4 cm.

• Question

  On a number line, the length of line segment joining iii and -3 is what?

  

  On a number line iii and -iii are each 3 units from cypher (in opposite directions). And so the total distance betwixt them is 3 + 3 = six.

• Question

  Would line AB exist the aforementioned as line BA?

  

  Yes.

• Question

  I don't sympathise the distance formula. Tin you help?

  

  It'south only the Pythagorean theorem. Find the vertical change (between endpoints of the line). Foursquare it. Find the horizontal change. Foursquare that, too. Add together the two squares. And so find the square root of that sum. This gives yous the line length you're looking for.

• Question

  If I know the length of the line and one of the endpoints, how do I detect the other endpoint?

  

  You can't do it unless you lot also know the slope of the line.

Show more answers

Inquire a Question

200 characters left

Include your email address to go a bulletin when this question is answered.

Submit

Advert

Video

• Remember the order of operations when calculating your answer. Subtract starting time, then foursquare the differences, then add, and then detect the square root.

• Practise not confuse this formula with others, similar the Midpoint Formula, Slope Formula, Equation of a Line or Line Formula.

Thank you for submitting a tip for review!

Advertising

About This Article

Commodity Summary X

To utilize the distance formula to find the length of a line, start by finding the coordinates of the line segment's endpoints. Then, plug the coordinates into the distance formula. Next, subtract the numbers in parenthesis and so foursquare the differences. In one case you lot've washed that, just add the numbers that are nether the radical sign and solve for d. To learn how to ready the distance formula, proceed reading!

Did this summary assistance you?

Thank you to all authors for creating a page that has been read 443,706 times.

Did this commodity assist you?

Source: https://www.wikihow.com/Use-Distance-Formula-to-Find-the-Length-of-a-Line

Posted by: williamsuniagard.blogspot.com

Share this post