Question

Use the following four coordinates to determine which one has a distance of 6 units from point E (3, 1). (5, 1) (2, 4) (3, 7) (7, 2)

Answer 1

Use the distance formula to find the distance between two points.
For any points
`P(x_1,\ y_1)` and
`Q(x_2,\ y_2)`, the distance between them
`PQ=√((x_2-x_1)^2+(y_2-y_1)^2)`


`EA=√((3-5)^2+(1-1)^2)=√((-2)^2+0^2)=√(4)=2`

`EB=√((3-2)^2+(1-4)^2)=√(1^2+(-3)^2)=√(1+9)=√(10)`

`EC=√((3-3)^2+(1-7)^2)=√(0^2+(-6)^2)=√(36)=6`

`ED=√((3-7)^2+(1-2)^2)=√((-4)^2+(-1)^2)=√(16+1)=√(17)`

The correct answer is C(3, 7).
(you don't even need to use the distance formula to realize this since it's 6 units directly above E(3, 1))