Respuesta :
Answer:
k = 3
Step-by-step explanation:
We have the distance formula: [tex]d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]. We can plug in [tex]4\sqrt{2}[/tex] = d, x2 = 6, x1=2, y2 = 7, y1 = k.
Then, we can solve the question using some algebra to find that k = 3.
Edit: Here is a step by step:
[tex]4\sqrt{2} = \sqrt{(6-2)^2 + (7-k)^2}\\[/tex]
[tex](4\sqrt{2})^2 = (6-2)^2 + (7-k)^2[/tex]
[tex]32 = (4)^2 + (7-k)^2[/tex]
[tex]32 = 16 + (7-k)^2[/tex]
[tex]32 - 16 = (7-k)^2[/tex]
[tex]16 = (7-k)^2[/tex]
[tex]\sqrt{16} = (7-k)[/tex]
[tex]4 = 7-k[/tex]
[tex]k = 3[/tex]
