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. Hypotenuse^{2}= (length of leg lying on the*x*-axis)^{2}+ (length of the leg parallel to the*y*-axis)^{2}= 6^{2}+ 2^{2}= 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!

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