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Tricks to learn Coordinate Geometry Video Lecture | Geometry for MAT
FAQs on Tricks to learn Coordinate Geometry Video Lecture - Geometry for MAT
| 1. How is the distance formula derived in coordinate geometry? |  |
Ans. The distance formula in coordinate geometry is derived using the Pythagorean theorem. It states that the square of the distance between two points (x1, y1) and (x2, y2) in a coordinate plane is equal to the sum of the squares of the differences in their coordinates. By taking the square root of this sum, we can calculate the distance between the two points.
| 2. Can the distance formula be used in three-dimensional space? | |
Ans. Yes, the distance formula can be extended to three-dimensional space. In three dimensions, the distance between two points (x1, y1, z1) and (x2, y2, z2) is calculated similarly using the Pythagorean theorem. The square of the distance is equal to the sum of the squares of the differences in the x, y, and z coordinates, and by taking the square root, we obtain the actual distance.
| 3. How is the distance formula used to find the length of a line segment? | |
Ans. To find the length of a line segment using the distance formula, we need to know the coordinates of the endpoints of the segment. By applying the distance formula, which involves finding the square root of the sum of the squares of the differences in the coordinates, we can determine the distance between the two endpoints. This distance represents the length of the line segment.
| 4. Is the distance formula applicable only to straight lines in coordinate geometry? | |
Ans. No, the distance formula is not limited to straight lines. It can be used to calculate the distance between any two points in a coordinate plane, regardless of whether they are connected by a straight line or not. The formula measures the shortest distance between the two points, which can be a straight line segment or a curve.
| 5. Can the distance formula be used to find the distance between a point and a line? | |
Ans. Yes, the distance formula can be employed to determine the shortest distance between a point and a line in coordinate geometry. By considering the coordinates of the given point and the equation of the line, we can use the distance formula to calculate the perpendicular distance between the point and the line. This distance represents the shortest distance between them.
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