Question

The points (4,2) and (-1, y) are √√74 units apart. What is the

value of y?


Please help!!!

Answer 1

y = - 5 or y = 9

Explanation:

using the distance formula

d =
`\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2 }`

with (x₁, y₁ ) = (4, 2 ) and (x₂, y₂ ) = (- 1, y )

d =
`√((-1-4)^2+(y-2)^2)`

=
`√((-5)^2+(y-2)^2)`

=
`√(25+(y-2)^2)`

equating to
`√(74)` , that is

`√(25+(y-2)^2)` =
`√(74)` ( square both sides )

25 + (y - 2)² = 74 ( subtract 25 from both sides )

(y - 2)² = 49 ( take square root of both sides )

y - 2 = ±
`√(49)` = ± 7 ( add 2 to both sides )

y = 2 ± 7

Then

y = 2 + 7 = 9 or y = 2 - 7 = - 5