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Point of intersection means the point at which two lines intersect. These two lines are represented by the equation a 1 x + b 1 y + c 1 = 0 and a 2 x + b 2 y + c 2 = 0, respectively. Given figure illustrate the point of intersection of two lines.
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The point of intersection formula is used to find the point of intersection of two lines, meaning the meeting point of two lines. These two lines can be represented by the equation \(a_1x + b_1y + c_1= 0\) and \(a_2x + b_2y + c_2 = 0\), respectively.
In geometry, an intersection is a point, line, or curve common to two or more objects (such as lines, curves, planes, and surfaces). The simplest case in Euclidean geometry is the line–line intersection between two distinct lines, which either is one point (sometimes called a vertex) or does not exist (if the lines are parallel).
When two lines share a common point, they are called intersecting lines. This common point that exists on all intersecting lines is called the point of intersection. The two non-parallel straight lines which are co-planar will have an intersection point.
- Find the point of intersection of line 3x + 4y + 5 = 0, 2x + 5y +7 = 0. The point of intersection of two lines is given by : (x, y) = ((b1*c2−b2*c1)/(a1*b2−a2*b1), (c1*a2−c2*a1)/(a1*b2−a2*b1))
- Find the point of intersection of line 9x + 3y + 3 = 0, 4x + 5y + 6 = 0. The point of intersection of two lines is given by : (x,y) = ((b1*c2−b2*c1)/(a1*b2−a2*b1), (c1*a2−c2*a1)/(a1*b2−a2*b1))
- Check if the two lines are parallel or not 2x + 4y + 6 = 0, 4x + 8y + 6 = 0. To check whether the lines are parallel or not we need to check a1/b1 = a2/b2.
- Check if the two lines are parallel or not 3x + 4y + 8 = 0, 4x + 8y + 6 = 0. To check whether the lines are parallel or not we need to check a1/b1 = a2/b2.
What is the point of intersection? The point of intersection is a unique point where two or more lines cross each other. In a two-dimensional coordinate system, this point has the same x and y coordinates on each of the intersecting lines.
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When two or more lines cross or meet each other in a plane, the lines are called intersecting lines. Intersecting lines share a common point called the point of intersection. In the figure below, lines p and q intersect at point O. So, point O is the point of intersection.
