Which of the following points has a distance of 3 from the point (–7, 4)? (1 point)
O (-7, -1)
O (4,4)
O (-10, 4)
○ (10, 4)
To find the distance between two points on a coordinate plane, we can use the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
For the given point (-7, 4) and the possible points, we can calculate their distances from (-7, 4):
1) Distance from (-7, -1):
d = √((-7 - (-7))^2 + (-1 - 4)^2)
= √(0^2 + (-5)^2)
= √(0 + 25)
= √25
= 5
2) Distance from (4, 4):
d = √((4 - (-7))^2 + (4 - 4)^2)
= √((4 + 7)^2 + 0^2)
= √(11^2 + 0)
= √(121 + 0)
= √121
= 11
3) Distance from (-10, 4):
d = √((-10 - (-7))^2 + (4 - 4)^2)
= √((-10 + 7)^2 + 0^2)
= √((-3)^2 + 0)
= √(9 + 0)
= √9
= 3
4) Distance from (10, 4):
d = √((10 - (-7))^2 + (4 - 4)^2)
= √((10 + 7)^2 + 0^2)
= √(17^2 + 0)
= √(289 + 0)
= √289
= 17
Out of the given options, the point (-10, 4) has a distance of 3 from the point (-7, 4).