Class 10 maths coordinate geometry
Understand the Problem
The question refers to coordinate geometry topics that are typically covered in Class 10 mathematics curriculum. This may involve understanding concepts like plotting points, understanding the Cartesian plane, calculating the distance between points, finding the midpoint, and the slope of a line.
Answer
The distance between two points $A(x_1, y_1)$ and $B(x_2, y_2)$ is $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.
Answer for screen readers
The distance between points $A(x_1, y_1)$ and $B(x_2, y_2)$ is given by: $$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$
Steps to Solve
- Identify Points on the Cartesian Plane
Start by identifying the coordinates of the two points. For example, let the first point be $A(x_1, y_1)$ and the second point be $B(x_2, y_2)$.
- Determine the Formula for Distance
The distance $d$ between two points in the Cartesian plane can be calculated using the distance formula: $$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$
- Calculate the Differences
Subtract the coordinates of point $A$ from those of point $B$ to find the differences:
- $x_2 - x_1$
- $y_2 - y_1$
- Square the Differences
Take the differences from the previous step and square them: $$ (x_2 - x_1)^2 $$ $$ (y_2 - y_1)^2 $$
- Sum the Squared Differences
Add the squared results together: $$ (x_2 - x_1)^2 + (y_2 - y_1)^2 $$
- Take the Square Root
Finally, take the square root of the sum to find the distance: $$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$
The distance between points $A(x_1, y_1)$ and $B(x_2, y_2)$ is given by: $$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$
More Information
The distance formula is derived from the Pythagorean theorem and is essential for determining how far apart two points are in a 2D space. It plays a key role in various applications, including physics, computer graphics, and navigation.
Tips
- Forgetting to square the differences before adding them.
- Neglecting the square root step to find the actual distance.
- Mixing up the coordinates ($x_1$ with $x_2$ or $y_1$ with $y_2$).
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