# Intersection of two lines calculator

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We will get through this together. Updated: August 5, References. With a couple extra techniques, you can find the intersections of parabolas and other quadratic curves using similar logic.

To algebraically find the intersection of two straight lines, write the equation for each line with y on the left side.

History of robots pptNext, write down the right sides of the equation so that they are equal to each other and solve for x. Write down one of the two equations again, substituting the previous answer in place of x, and solve for y. These answers will give you the x and y coordinates of the intersection. To learn how to find the intersection when working with quadratic equations, keep reading!

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Article Edit. Learn why people trust wikiHow. To create this article, 19 people, some anonymous, worked to edit and improve it over time. Together, they cited 6 references. This article has also been viewedtimes. Learn more Problems with Quadratic Equations. Tips and Warnings. Related Articles. Article Summary. Method 1 of Remember, you can cancel out terms by performing the same action to both sides.

If you do not know the equations, find them based on the information you have. Set the right sides of the equation equal to each other. Write a new equation that represents this. Solve for x. Solve this using algebra, by performing the same operation on both sides. If this is impossible, skip down to the end of this section.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. The dark mode beta is finally here.

Change your preferences any time. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. I have dynamically generated lines that animate and I want to detect when a lines hits another. I'm trying to implement some basic linear algebra to obtain the equation of the lines and then solving for x,y, but the results are erratic.

At this point I'm testing only with two lines which means I should be getting one point of intersection, but I get two. I just want to make sure my math is ok and that I should be looking elsewhere for the problem. The problem is that I'm getting two different values for the point of intersection.

There should only be one, which leads me to believe my calculations are wrong. Yes, x2,y2,x4,y4 are all moving, but they have a set angle and the consistent slopes confirm that. I found a great solution by Paul Bourke. Here it is, implemented in JavaScript:. For line segment-line segment intersections, use Paul Borke's solution :.

For infinite line intersections, use Justin C. Round's algorithm :. There is an npm module that does just that: line-intersect. Learn more. Asked 7 years, 4 months ago. Active 1 month ago. Viewed 15k times. PI, false ; context. Adam Adam 8, 16 16 gold badges 63 63 silver badges bronze badges. Please add a short self-contained examplewhich shows the problem. At the moment your post is both lacking a problem and a question, it should contain at least one of them.

Note: you told us that the result is erratic, but you didn't tell us the exact nature of the problem. The fact that you keep checking whether things are positive is a red flag. This should not be necessary. Also, you are definitely not taking care of the case where one of the lines is vertical i.

Aaron, my approach was to do it as if a human were trying to solve for the variables. What would be a more efficient method?

Egg incubator temperature controller circuitActive Oldest Votes.First of all, let us assume that we have two points x 1y 1 and x 2y 2. Now, we find the equation of line formed by these points. We have to now solve these 2 equations to find the point of intersection. To solve, we multiply 1. This gives us the value of x. Similarly, we can find the value of y.

Note: This gives the point of intersection of two lines, but if we are given line segments instead of lines, we have to also recheck that the point so computed actually lies on both the line segments. If the line segment is specified by points x 1y 1 and x 2y 2then to check if x, y is on the segment we have to just check that. These can be derived by first getting the slope directly and then finding the intercept of the line. This article is contributed by Aanya Jindal.

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Writing code in comment? Please use ide. To find the point of. This is simplified. Here, we have considered AB. MaxValue, double.

### Finding intersection point of the lines

MaxValue. Improved By : shrikanth Load Comments.The intersection is the place x,y where two functions cross each other on a graph. You may want to find the intersection of two lines for many reasons. Perhaps the most important reason is that the intersection of two graphs is the solution to a series of equations which is much easier than solving systems of equations algebraically!

Three ways to find the intersection of two lines click to skip to that section :. An intersection is where two or more functions meet on a graph. Finding an intersection is one way to solve a system of equations ; the point where the two graphs cross each other intersect is the solution to the system. Using a TI 89 to find the intersection is much faster than the hand method and is no harder than pressing a few buttons.

Step 5: Enter the second function. Step 8: View the graph by pressing the diamond key and then F3. You will see that the two graphs intersect. Step For the lower bound, press the left arrow, moving the arrow to the left of the intersection.

Health chapter 19 assessment answersThe intersection of these two graphs is -1,5. Step 1: Press F3 for the Trace feature. Step 2: Press the left arrow or the right arrow to trace along the graph. Change which graph you trace along by pressing the up or down arrows. Step 1: Set the equations equal to each other. The x-intersection is Step 3: Use the value you found in Step 2 to find y. If you find the intersection of two lines by hand, you can use an online graphing calculator to check your work.

This free online calculator works much in the same way as the TI albeit with stripped down features. Step 2: Input your two equations. The following image shows what the calculator looks like after the equations have been entered:. You can see the intersection of the two lines at the bottom left of the image.To find the intersection of two straight lines: First we need the equations of the two lines. Then, since at the point of intersection, the two equations will have the same values of x and y, we set the two equations equal to each other.

This gives an equation that we can solve for x We substitute that x value in one of the line equations it doesn't matter which and solve it for y. This gives us the x and y coordinates of the intersection. In the case of two non-parallel lines, the intersection will always be on the lines somewhere.

But in the case of line segments or rays which have a limited length, they might not actually intersect. In Fig 1 we see two line segments that do not overlap and so have no point of intersection. However, if you apply the method above to them, you will find the point where they would have intersected if extended enough. In the interest of clarity in the applet above, the coordinates are rounded off to integers and the lengths rounded to one decimal place.

This can cause calculatioons to be slightly off. Home Contact About Subject Index. The point of intersection of two non- parallel lines can be found from the equations of the two lines. Try this Drag any of the 4 points below to move the lines. Note where they intersect. Fig 1. Segments do not intersect.The intersection point is determined by solving the values of x and y from the two lines equations by Cramer's rule or by direct substitution:.

The intersection point is determined by solving the values of x and y from the two lines equations:.

**Solving a System of Equations Using Elimination and Multipliers**

The intersection point xy is found by the equations:. Angle bisector line equation expressed by m 1 and m 2 is:. The distance d of any common point xy on the angle bisector between two lines are the same two similar triangles. The angle between the lines is found by vector dot product method. In order to find the angle bisector line equation we use the distance equations:. Two lines intersection calculator.

Line 1. Angle Bisector lines. Degree Radian. Inclined lines. Two lines intersection. Solving the lines equations for x and y by Cramer's rule.

Two lines angle bisector. The angle of the lines angle bisector from the x axis is: The equation of the angle bisector line is: First line:.

Two lines angle bisector example.

Example 3 - intersection of 2 lines each defined by 2 points. Find the intersection point of two lines each of them defined by two pair of coordinates, first line by x 1 y 1 x 2 y 2 and second line by x 3 y 3 and x 4 y 4. And the solution is:. And the same process accompanied with some basic algebra steps we get the y coordinate:.This online calculator finds and displays the point of intersection of two lines given by the equations in general form.

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