To find the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ in a coordinate plane, we use the distance formula:

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

For the points $(3, 7)$ and $(5, 0)$:

• $x_1 = 3$, $y_1 = 7$
• $x_2 = 5$, $y_2 = 0$

Plugging these values into the formula:

$d = \sqrt{(5 - 3)^2 + (0 - 7)^2}$ $d = \sqrt{(2)^2 + (-7)^2}$ $d = \sqrt{4 + 49}$ $d = \sqrt{53}$ $d \approx 7.28$

Thus, the distance between the points $(3, 7)$ and $(5, 0)$ is approximately $7.28$.

Would you like more details or have any questions?

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1. What is the significance of using the distance formula in coordinate geometry?
2. How would you find the midpoint between two points?
3. How does the distance formula relate to the Pythagorean theorem?
4. What happens to the distance formula in three-dimensional space?
5. Can the distance formula be used with points that have non-integer coordinates?

Tip: Remember, in coordinate geometry, the distance formula is derived from the Pythagorean theorem applied to the horizontal and vertical distances between points.