To find the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) on a coordinate plane, we can use the distance formula, which is derived from the Pythagorean theorem:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Let's apply this to each question.
Question 1: Finding the distance between points \((-2, 3)\) and \((-7, -9)\)
We have: \[ x_1 = -2, \quad y_1 = 3, \quad x_2 = -7, \quad y_2 = -9 \]
Calculating the differences: \[ x_2 - x_1 = -7 - (-2) = -7 + 2 = -5 \] \[ y_2 - y_1 = -9 - 3 = -12 \]
Now, substituting into the distance formula: \[ d = \sqrt{(-5)^2 + (-12)^2} = \sqrt{25 + 144} = \sqrt{169} = 13 \]
So the answer for Question 1 is C 13.
Question 2: Finding the distance between points \((4, 6)\) and \((-2, -2)\)
We have: \[ x_1 = 4, \quad y_1 = 6, \quad x_2 = -2, \quad y_2 = -2 \]
Calculating the differences: \[ x_2 - x_1 = -2 - 4 = -6 \] \[ y_2 - y_1 = -2 - 6 = -8 \]
Now, substituting into the distance formula: \[ d = \sqrt{(-6)^2 + (-8)^2} = \sqrt{36 + 64} = \sqrt{100} = 10 \]
None of the options we have listed correspond to our result of 10. Please check the options again, as the calculated distance is 10 based on the given points.
However, based on the closest option provided, we would be looking at the correct answer as not listed. Please confirm if options are correctly stated or revised.
In summary:
- Question 1 answer: C 13.
- Question 2 answer: not listed correctly; result is 10.