#### A coordinate grid is the most important part of coordinate geometry. It has one horizontal line and one vertical line that is usually known as axes. These two lines intersect each other at a common point that is known as the origin. The entire plane is divided into small squares and in four quadrants. This entire setting is known as the coordinate grid.
Now, if there is a line segment on the coordinate grid, how will you find its length?
Well, there are two methods of doing that; the first one is to use the Pythagoras theorem, and the second one is to use the distance formulae. Both of these methods are suitable for different situations.
**CASE I: Slanted Line Segment** -
When you have a line segment, you can extend a vertical and a horizontal line from its endpoint to complete a right-angle triangle. Now, count the units covered by the base and the perpendicular of the triangle and insert the values in the following formula;
P^{2} + B^{2} = H^{2}.
Here P is the length of the perpendicular, B is the length of the base, and H is the unknown length of the slanted line segment. You can find the length of the line through this formula.
Another method to solve this is through the distance formula. Start by identifying the endpoints of the line segments. You will get two points such as (x_{1} , y_{1}) and (x_{2}, y_{2}). Once you have these points, you need to substitute the values in the following formula;
AB = √(x_{1}- x_{2})^{2} + (y_{1} - y_{2})^{2})
**CASE II: Straight Line (vertical/horizontal)** - When you have a simple straight line on the coordinate grid, calculating the length is simple; you just have to count the units that the line covers, and if there is a scale mentioned, you can multiply it with the value of each unit represents.
If you do not want to do that, you can always choose to use the distance formula.

In these worksheets, students will work with notional coordinate grids to find the length of segments using a trigonometric equation. Problems are presented as word problems, and students will be required to write the problem as an equation and then solve. The endpoints provided include both positive and negative numbers. Extra paper may be required in order for students to do their calculations. This set of worksheets contains lessons, step-by-step solutions to sample problems, both simple and more complex problems, a review, and a quiz. It also includes ample worksheets for students to practice independently. Most worksheets contain between eight and ten problems. When finished with this set of worksheets, students will be able to find the length of a line segment with specified endpoints. These worksheets explain how to find the length of a line segment with specified endpoints. Sample problems are solved and practice problems are provided.