CP #4

This is a Kaplan Problem Solving Challenge question. It's a 25 minute quiz with 16 questions. I finished it just in time, but I got 2/16 wrong. Here's the first one:


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

	4
	8

Answer Explantion:

Don't try to keep all the information in your head - add to the diagram so you can refer to it as you solve. Horizontal line y = 4 is the perpendicular bisector of JK, so JK must be vertical and parallel to the y-axis. Draw in segment JK, dropping straight down from point J through the x-axis. Before you can find the distance from the origin to point K, you need to know its coordinates. K is directly below J so both points are the same distance from the y-axis and their x-coordinates must be the same. So the x-coordinate of K is 6. Since the line y = 4 bisects JK, the vertical distance from J to the line must be the same as the vertical distance from the line to K. Vertical distance is the difference between the y-coordinates, so the vertical distance from J to line y = 4 is 10 - 4, or 6. Therefore the difference between the y-coordinates of line y = 4 and point K is also 6, so the y-coordinate of K = 4 - 6, making -2 the y-coordinate of point K. So the coordinates of point K are (6, -2). You will notice that K, the origin O, and the point where JK crosses the x-axis is a right triangle, with its hypotenuse being the distance from the origin to point K. Use the Pythagorean theorem to find the length of the hypotenuse. Hypotenuse² = (length of leg lying on the x-axis)² + (length of the leg parallel to the y-axis)² = 6² + 2² = 40. So the distance from the origin to K =  = .

What I did wrong

1. Didn't remember distance formula

2. Made a mistake in considering K (6,0) since I didn't realise that my K to line y=4 was only 4 points away, not 6.

Wow, this is a first! Didn't remember the formula, AND made a silly mistake!