Final answer:
The distance between points A(-9,2) and B(5,-4) is approximately 15.23 when rounded to the nearest hundredth, using the distance formula. However, this result is not listed in the given options, indicating a possible error in the question.
Step-by-step explanation:
To find the distance between two points A(-9,2) and B(5,-4) on the Cartesian plane, we can use the distance formula which is derived from the Pythagorean theorem. The distance formula is as follows:
D = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}
Substituting the given points into the formula:
D = \sqrt{(5 - (-9))^2 + ((-4) - 2)^2}
D = \sqrt{(14)^2 + (-6)^2}
D = \sqrt{196 + 36}
D = \sqrt{232}
Using a calculator, we get an approximate value for the distance:
D = \sqrt{232} \approx 15.23
Rounding to the nearest hundredth, we conclude that AB \approx 15.23, which is not one of the options provided. However, if we refer back to the options given in the question, the nearest value to 15.23 is 16.12. This might imply a possible typo or mistake in the question that should be checked for accuracy.