Question

Which of the following has a distance of 3 from the point (-7, 4)?
(4, 4)
(-10, 4)
(-7, -1)
(10, 4)

Answer 1

To find which of the given points is a distance of 3 from the point (-7, 4), we can use the distance formula. The distance \( d \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

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

In this case, we have the point \((-7, 4)\) and we want to check the distance from this point to each of the given points.

1. **For the point (4, 4)**:
\[
d = \sqrt{(4 - (-7))^2 + (4 - 4)^2} = \sqrt{(4 + 7)^2 + 0^2} = \sqrt{11^2} = 11
\]

2. **For the point (-10, 4)**:
\[
d = \sqrt{(-10 - (-7))^2 + (4 - 4)^2} = \sqrt{(-10 + 7)^2 + 0^2} = \sqrt{(-3)^2} = 3
\]

3. **For the point (-7, -1)**:
\[
d = \sqrt{(-7 - (-7))^2 + (-1 - 4)^2} = \sqrt{0^2 + (-1 - 4)^2} = \sqrt{0 + (-5)^2} = 5
\]

4. **For the point (10, 4)**:
\[
d = \sqrt{(10 - (-7))^2 + (4 - 4)^2} = \sqrt{(10 + 7)^2 + 0^2} = \sqrt{17^2} = 17
\]

Among the calculated distances, only the point \((-10, 4)\) has a distance of 3 from the point \((-7, 4)\).

Thus, the answer is:
\[
\text{(-10, 4)}
\]