What are the two possible values of K given a specific distance from a point?

[Mo]

I have managaed to do all of the questions upto this one without getting an answer wrong .. but this question .. i just don't quite understand it.

"The point (3 , k) is a distance of 5 units from (0, 1) .

Find the two possible values of K"

What exactly do they mean by "5 units"

I am thinking that i am going to need to compare the length (3,k) to (0 ,1) plus "5 units" .And then solve for K

I don't need an answer, i need the question (push in the right direction would be nice)

Regards,
Mo

PS: Also .. rather unrelated .. what exactly is K-12 ... because I am in college in UK .. but I am 16 (usual age when people enter college in UK) should my question be posted here in k-12 .. or "Homework:College level"?

 

[HallsofIvy]

To answer you last question first: In the United States, children normally start in "kindergarten" (A German word!) at age five and then continue through 12 years (1st grade to 12th) so that they are typically 18 years old when they go to college.


Now, for your mathematical question.

"The point (3 , k) is a distance of 5 units from (0, 1) .

Find the two possible values of K"

What exactly do they mean by "5 units"

What do they mean by (0,1) or (3,k)? The point (0,1) is on the y-axis exactly 1 "unit" above the x axis. The point (3,k) is three "units" to the right of the y-axis and k "units" from the x-axis. A "unit" is whatever units (mm, meter, inch, mile or made up unit) are used to mark the axes.

'I am thinking that i am going to need to compare the length (3,k) to (0 ,1) plus "5 units" '

No, (3,k) is a point- it does not have a length! The line segment from (3,k) to (0,1) has a length: $\sqrt{(3-0)^2+ (k-1)^2}$. Set THAT equal to 5 and solve for k. (hint: first thing you should do is square both sides). That will give you a quadratic equation which has two solutions.

You could do this geometrically: the set of all points which have distance 5 from (0,1) is the circle with radius 5 and center (0,1). That circle will cross the line x= 3 in two places. k is the y coordinate of those two places.

 

[Mo]

Thanks for your help, most appreciated.I got the answer in the end (k=-3, k=5) which is correct according to the answers.I guess its better for me to post in here! thanks again.

Regrads,
Mo