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Mind Map: Coordinate Geometry | Mathematics (Maths) Class 10 PDF Download
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FAQs on Mind Map: Coordinate Geometry - Mathematics (Maths) Class 10
| 1. What is the distance formula in coordinate geometry? |  |
Ans. The distance formula is used to determine the distance between two points in a coordinate plane. If you have two points, \( (x_1, y_1) \) and \( (x_2, y_2) \), the distance \( d \) between them can be calculated 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 \( M \) of the line segment connecting two points \( (x_1, y_1) \) and \( (x_2, y_2) \) can be found using the midpoint formula:
\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
This gives the average of the x-coordinates and the y-coordinates of the two points.
| 3. What is the slope of a line in coordinate geometry, and how is it calculated? | |
Ans. The slope \( m \) of a line measures its steepness and direction. It is calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
where \( (x_1, y_1) \) and \( (x_2, y_2) \) are two distinct points on the line. A positive slope indicates an upward trend, while a negative slope indicates a downward trend.
| 4. How can I determine the equation of a line given two points? | |
Ans. To find the equation of a line given two points \( (x_1, y_1) \) and \( (x_2, y_2) \), first calculate the slope \( m \) using the slope formula. Then, use the point-slope form of the equation:
\[ y - y_1 = m(x - x_1) \]
You can rearrange this to slope-intercept form \( y = mx + b \) if needed.
| 5. What are the different forms of the equation of a line in coordinate geometry? | |
Ans. There are several forms of the equation of a line:
1. <b>Slope-intercept form:</b> \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
2. <b>Point-slope form:</b> \( y - y_1 = m(x - x_1) \), used when you know a point on the line and the slope.
3. <b>Standard form:</b> \( Ax + By = C \), where \( A \), \( B \), and \( C \) are integers, and \( A \) should be non-negative.
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