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Point of intersection means the point at which two lines intersect. These two lines are represented by the equation a1x + b1y + c1= 0 and a2x + b2y + c2 = 0, respectively. Given figure illustrate the point of intersection of two lines. We can find the point of intersection of three or more lines also. By solving the two equations, we can find ...
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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 a1x+b1y+c1 = 0 a 1 x + b 1 y + c 1 = 0 and a2x+b2y+c2 = 0 a 2 x + b 2 y + c 2 = 0, respectively. It is possible to find the point of intersection of three or more lines.
Intersection of two lines is a point at which both lines meet. 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.
The point of intersection (common point) is the ordered pair (0, 0). In this next example, the two lines on the coordinate plane do not have any common point of intersection. They are considered to be parallel lines which means they are non-intersecting lines.
- 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.
One method to find the point of intersection is to substitute the value for y of the 2 nd equation into the 1 st equation and solve for the x-coordinate. -x + 6 = 3x - 2. -4x = -8. x = 2. Next plug the x-value into either equation to find the y-coordinate for the point of intersection. y = 3×2 - 2 = 6 - 2 = 4. So, the lines intersect at (2, 4).
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Oct 5, 2024 · This point of intersection is called the point of intersection. The formula of the Point of the intersection of two lines. If the equations of two non-parallel lines are. L 1 = a 1 x + b 1 y + c 1 = 0 L 2 = a 2 x + b 2 y + c 2 = 0. If P (x 1, y 1) is a point of intersection of L 1 and L 2, then solving these two equations of the line by cross ...
