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 the distance formula in coordinate geometry? |  |
Ans. The distance formula is used to calculate the distance between two points in the coordinate plane. If you have two points \( (x_1, y_1) \) and \( (x_2, y_2) \), the distance \( d \) between them can be found using the formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}. \]
| 2. How do you find the midpoint between two points in coordinate geometry? | |
Ans. The midpoint \( M \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is calculated using the formula:
\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right). \]
This gives you the coordinates of the point that is exactly halfway between the two points.
| 3. What is the slope of a line in coordinate geometry? | |
Ans. The slope of a line measures its steepness and is calculated as the ratio of the rise (change in \( y \)) over the run (change in \( x \)). If you have two points \( (x_1, y_1) \) and \( (x_2, y_2) \), the slope \( m \) can be found using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1}. \]
| 4. How do you write the equation of a line in slope-intercept form? | |
Ans. The slope-intercept form of a line's equation is expressed as:
\[ y = mx + b, \]
where \( m \) is the slope of the line and \( b \) is the y-intercept (the point where the line crosses the y-axis). To write an equation in this form, you need to know the slope and the y-intercept.
| 5. What are the conditions for two lines to be parallel in coordinate geometry? | |
Ans. Two lines are parallel in coordinate geometry if they have the same slope. If the equations of the lines are in slope-intercept form \( y = m_1x + b_1 \) and \( y = m_2x + b_2 \), the lines are parallel if \( m_1 = m_2 \) and \( b_1 \neq b_2 \).
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