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

Responses

(−10, 4)
Left Parenthesis negative 10 comma 4 Right Parenthesis

(−7, −1)
Left Parenthesis negative 7 comma negative 1 Right Parenthesis

(10, 4)
Left Parenthesis 10 comma 4 Right Parenthesis

(4, 4)

1 answer

To find the distance between two points, you can use the distance formula:

d = √((x2 - x1)^2 + (y2 - y1)^2)

The given point is (-7, 4). Let's calculate the distance from this point to each of the options:

1. (-10, 4):
d = √((-10 - (-7))^2 + (4 - 4)^2)
= √((-3)^2 + 0^2)
= √(9 + 0)
= √9
= 3

2. (-7, -1):
d = √((-7 - (-7))^2 + (-1 - 4)^2)
= √((0)^2 + (-5)^2)
= √(0 + 25)
= √25
= 5

3. (10, 4):
d = √((10 - (-7))^2 + (4 - 4)^2)
= √((17)^2 + (0)^2)
= √(289 + 0)
= √289
= 17

4. (4, 4):
d = √((4 - (-7))^2 + (4 - 4)^2)
= √((11)^2 + (0)^2)
= √(121 + 0)
= √121
= 11

So, the point with a distance of 3 from the point (-7, 4) is (-10, 4).