Question

Please help thank you so much

Answer 1

d = 2
`√(5)` ≈ 4.47

Explanation:

to find the point of intersection A between the 2 lines, equate them, that is

y = x - 6 → (1)

y = -
`(1)/(2)` x → (2)

x - 6 = -
`(1)/(2)` x ( multiply through by 2 to clear the fraction )

2x - 12 = - x ( add x to both sides )

3x - 12 = 0 ( add 12 to both sides )

3x = 12 ( divide both sides by 3 )

x = 4

substitute x = 4 into either of the 2 equations and solve for y

substituting into (1)

y = 4 - 6 = - 2

A = (4, - 2)

calculate the distance d using the distance formula

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

with (x₁, y₁ ) = A(4, - 2) and (x₂, y₂ ) = O(0, 0 )

d =
`√((0-4)^2+(0-(-2))^2)`

=
`√((-4)^2+(0+2)^2)`

=
`√(16+2^2)`

=
`√(16+4)`

=
`√(20)`

=
`√(4(5))`

=
`√(4)` ×
`√(5)`

= 2
`√(5)`

≈ 4.47 ( to 2 decimal places )