Question

Which of the following points has a distance of 10 from the point (−1, 2) ? Responses (10, 2) (10, 2) - no response given (−1, −12) (−1, −12) - no response given (−11, 2) (−11, 2) - no response given (−1, 10) (−1, 10) - no response given

Answer 1

To find which of the given points has a distance of 10 from the point \((-1, 2)\), we can use the distance formula, which is given by:

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

where \((x_1, y_1)\) is the point \((-1, 2)\) and \((x_2, y_2)\) is the point we are checking.

Let's check each point:

1. **Point (10, 2)**:
\[
d = \sqrt{(10 - (-1))^2 + (2 - 2)^2} = \sqrt{(11)^2 + 0^2} = \sqrt{121} = 11
\]
(Distance is 11)

2. **Point (-1, -12)**:
\[
d = \sqrt{(-1 - (-1))^2 + (-12 - 2)^2} = \sqrt{(0)^2 + (-14)^2} = \sqrt{196} = 14
\]
(Distance is 14)

3. **Point (-11, 2)**:
\[
d = \sqrt{(-11 - (-1))^2 + (2 - 2)^2} = \sqrt{(-10)^2 + 0^2} = \sqrt{100} = 10
\]
(Distance is 10)

4. **Point (-1, 10)**:
\[
d = \sqrt{(-1 - (-1))^2 + (10 - 2)^2} = \sqrt{(0)^2 + (8)^2} = \sqrt{64} = 8
\]
(Distance is 8)

From these calculations, we find that the point **(-11, 2)** has a distance of **10** from the point \((-1, 2)\).