To find the distance between the points \( (2, 3) \) and \( (-4, -9) \), we can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Where \( (x_1, y_1) = (2, 3) \) and \( (x_2, y_2) = (-4, -9) \).
Plugging the coordinates into the formula:
\[ d = \sqrt{((-4) - 2)^2 + ((-9) - 3)^2} \]
Calculating each part:
- \( (-4 - 2) = -6 \)
- \( (-9 - 3) = -12 \)
Now squaring these differences:
\[ d = \sqrt{(-6)^2 + (-12)^2} \] \[ = \sqrt{36 + 144} \] \[ = \sqrt{180} \]
Now, simplifying \( \sqrt{180} \):
\[ \sqrt{180} = \sqrt{36 \times 5} = 6\sqrt{5} \]
Now, using a calculator to find the decimal value:
\[ 6\sqrt{5} \approx 6 \times 2.236 = 13.416 \]
Finally, rounding to the nearest hundredth:
\[ \approx 13.42 \]
Therefore, the distance between the points \( (2, 3) \) and \( (-4, -9) \) is approximately 13.42.
1 answer