The coordinate plane is really important for figuring out distances and midpoints in geometry.
It has two lines that cross each other at right angles: the x-axis (horizontal line) and the y-axis (vertical line).
Key Ideas:
Distance Formula: To find the distance ( d ) between two points, like ( (x_1, y_1) ) and ( (x_2, y_2) ), you can use this formula: [ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} ]
This means you subtract the x-coordinates and the y-coordinates, square those results, add them together, and then take the square root.
Midpoint Formula: The midpoint ( M ) between two points ( (x_1, y_1) ) and ( (x_2, y_2) ) is found with this formula: [ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) ]
Here, you add the x-coordinates and divide by 2, and do the same for the y-coordinates. This gives you the middle point between those two points.
By understanding these formulas, students can easily find distances and midpoints on the coordinate plane. This helps improve their geometry skills!
The coordinate plane is really important for figuring out distances and midpoints in geometry.
It has two lines that cross each other at right angles: the x-axis (horizontal line) and the y-axis (vertical line).
Key Ideas:
Distance Formula: To find the distance ( d ) between two points, like ( (x_1, y_1) ) and ( (x_2, y_2) ), you can use this formula: [ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} ]
This means you subtract the x-coordinates and the y-coordinates, square those results, add them together, and then take the square root.
Midpoint Formula: The midpoint ( M ) between two points ( (x_1, y_1) ) and ( (x_2, y_2) ) is found with this formula: [ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) ]
Here, you add the x-coordinates and divide by 2, and do the same for the y-coordinates. This gives you the middle point between those two points.
By understanding these formulas, students can easily find distances and midpoints on the coordinate plane. This helps improve their geometry skills!