Perp Bisector

Since y = 4 is perpendicular bisector, so it meets line JK at (6,4) and k would be 6 units below. this k is (6, - 2).
This distnace of K from origin = Sqrt(6^2 + -2^2) = 2sqrt10

stubbornp wrote:In the diagram,the line y=4 is the perpendicular bisector of segment JK(not shown).What is the distance from origin to point K?

A. 4
B. 2sqrt(10)
3. 8
4. 6sqrt(2)
5. 4sqrt(34)

why k would be 6 units below?

Its because y=4 is the perpendicular bisector of JK and hence it will divide JK into equal halves @90 degree. The 1st 1/2 is from J to the point of intersection of y=4 with JK (the 1st 1/2 distance is 6 units). The 2nd 1/2 is from point of intersection of y=4 to K which shud also be 6 units since its a perpendicular bisector. Hence it will be 6 units down in the -ve direction of y-axis which is @-2.Thus K is 6, -2 and the distance is sqrt(36+4)

Also note that they haven't mentioned JK in the question, its only a line segment.

-Deepak

ok got it.....tnx all

stubbornp wrote:In the diagram,the line y=4 is the perpendicular bisector of segment JK(not shown).What is the distance from origin to point K?

A. 4
B. 2sqrt(10)
3. 8
4. 6sqrt(2)
5. 4sqrt(34)

It's really tricky question.

Key concept : Perpendicular bisector divides the line into two equal parts.

Here is the solution in a diagrammatic format. [/img]

he perpendicular bisector intersects line JK right through the midpoint. Since the distance from line y to point J is 6, this means that point K has coordinates (6,-2).

Plug the coordinates of point K into the distance equation:

c² = 6² + 2²
c² = 36 + 4
c² = 40
c = 2√10

The distance from point K to the origin is 2√10