Graph a line that is perpendicular to the given line. Determine the slope of the given line and the one you graphed in simplest form. Click and drag on the graph to draw a line. Click and drag to plot a perpendicular line. The line will change colors when a parallel or perpendicular line is drawn accurately. 10 6. 81 4 3. -10 9 -8-7 -6 -54 3 2 4 5 6 7 89 10 -8 P Type here to search
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
![### Graphing Perpendicular Lines
#### Instructions:
To graph a line that is perpendicular to a given line, follow these steps:
1. **Identify the Slope of the Given Line:**
- Determine the slope of the given line by finding the rise over run (change in y over change in x) between two points on the line.
2. **Calculate the Slope of the Perpendicular Line:**
- The slope of the line perpendicular to the given line is the negative reciprocal of the slope of the given line. If the slope of the given line is \( m \), then the slope of the perpendicular line will be \( -\frac{1}{m} \).
3. **Graph the Perpendicular Line:**
- Use the calculated slope to graph the perpendicular line by starting at any point on the graph, and applying the slope to determine the direction and steepness of the line.
#### Example:
In the graph below, a line is provided. Follow the instructions to draw a line that is perpendicular to this given line.
**Graph Description:**
- The given image shows a Cartesian coordinate system with a grid.
- The blue line plotted on the graph passes through points (-1, -5) and (6, 8).
**Steps to Graph Perpendicular Line:**
- The slope \( m \) of the given blue line can be calculated as follows:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8 - (-5)}{6 - (-1)} = \frac{13}{7} \]
- The slope of the perpendicular line will be the negative reciprocal:
\[ m_{\text{perpendicular}} = -\frac{1}{m} = -\frac{1}{\frac{13}{7}} = -\frac{7}{13} \]
- To draw the perpendicular line using the calculated slope, start from any convenient point on the graph and apply the slope \( -\frac{7}{13} \) to plot the line.
**Interactive Graph Feature:**
- Click and drag to plot a perpendicular line.
- The line will change colors when a parallel or perpendicular line is drawn accurately.
This interactive feature will help you visualize and confirm the accuracy of your perpendicular line graphing.
Practice by plotting the perpendicular line on the graph provided using the steps outlined above.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5ecc50c4-77d9-4125-8dac-49be2c236cb2%2F7b9e8026-f01d-414d-891b-35ce46550b53%2F6pvdbfl_processed.jpeg&w=3840&q=75)
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