Answer:
7.7
Step-by-step explanation:
To find the intersection points of the line and the circle we have to set up a system with their equations and solve. The system would look like this:
[tex]\left \{ {{x=1 } \atop {x^2+y^2=16}} \right.[/tex]
To solve, substitute 1 for x in the second equation to get:
[tex]1^2+y^2=16[/tex]
Solving, we get:
[tex]y=\sqrt{15}, y=-\sqrt{15}[/tex]
Therefore, the two points of intersection are [tex](1,\sqrt{15} )[/tex] and [tex](1,-\sqrt{15})[/tex]. The distance between these two points (the length of the chord in the circle) is [tex]2\sqrt{15}[/tex] which is 7.745966692414... which is 7.7 rounded to the nearest tenth.
Hope this helps :)
