Class 10 Exam > Class 10 Notes > Mathematics (Maths) Class 10 > Facts that Matter: Coordinate Geometry
Facts that Matter: Coordinate Geometry | Mathematics (Maths) Class 10 PDF Download
Facts that Matter
- Distance Formula
I. The distance between two points P (x1, y1) and Q (x2, y2) is given by
II. The distance of P (x, y) from the origin is - Section Formula
I. If P (x, y) divides the line segment AB, joining the points A (x1, y1) and B (x2, y2) in the ratio m : n, then
II. The coordinates (x, y) of the mid-point of PQ are given by:
III. If A (x1, y1), B (x2, y2) and C (x3, y3) be the vertices of ΔABC, then the coordinates G (x, y) of the centroid of ΔABC are:
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FAQs on Facts that Matter: Coordinate Geometry - Mathematics (Maths) Class 10
| 1. What is coordinate geometry? |  |
Ans. Coordinate geometry is a branch of mathematics that deals with the study of geometrical figures using a coordinate system. It involves representing points, lines, curves, and shapes in a plane using numerical coordinates.
| 2. How to find the distance between two points in coordinate geometry? | |
Ans. The distance between two points in coordinate geometry can be found using the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by the formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
| 3. What is the slope of a line in coordinate geometry? | |
Ans. The slope of a line in coordinate geometry represents its steepness or inclination. It is calculated by taking the ratio of the vertical change (change in y-coordinates) to the horizontal change (change in x-coordinates) between two points on the line.
The formula to find the slope of a line passing through two points (x1, y1) and (x2, y2) is given by:
Slope = (y2 - y1) / (x2 - x1)
| 4. How to find the equation of a line in coordinate geometry? | |
Ans. The equation of a line in coordinate geometry can be found using different methods, depending on the given information. One common method is using the slope-intercept form, which states that the equation of a line with slope 'm' and y-intercept 'b' is given by:
y = mx + b
Another method is using the point-slope form, which states that the equation of a line passing through a point (x1, y1) with slope 'm' is given by:
y - y1 = m(x - x1)
| 5. How to determine if two lines are parallel or perpendicular in coordinate geometry? | |
Ans. Two lines are parallel if and only if their slopes are equal. In other words, if the slopes of two lines are equal, the lines will never intersect and are considered parallel.
Two lines are perpendicular if and only if the product of their slopes is -1. In other words, if the slopes of two lines multiplied together yield -1, the lines will intersect at a right angle and are considered perpendicular.
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