To find which of the given points has a distance of 3 from the point (-7, 4), we can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
In this case, \( (x_1, y_1) = (-7, 4) \) and we need to check each option to see if the distance \( d \) equals 3.
Option 1: (−10, 4)
\[ d = \sqrt{((-10) - (-7))^2 + (4 - 4)^2} = \sqrt{(-3)^2 + 0^2} = \sqrt{9} = 3 \] This point is 3 units away.
Option 2: (4, 4)
\[ d = \sqrt{(4 - (-7))^2 + (4 - 4)^2} = \sqrt{(11)^2 + 0^2} = \sqrt{121} = 11 \] This point is not 3 units away.
Option 3: (−7, −1)
\[ d = \sqrt{((-7) - (-7))^2 + (-1 - 4)^2} = \sqrt{(0)^2 + (-5)^2} = \sqrt{25} = 5 \] This point is not 3 units away.
Option 4: (10, 4)
\[ d = \sqrt{(10 - (-7))^2 + (4 - 4)^2} = \sqrt{(17)^2 + 0^2} = \sqrt{289} = 17 \] This point is not 3 units away.
The only point that has a distance of 3 from the point (-7, 4) is:
(−10, 4).