800GMAT wrote:Thanks jayhawk..... can u also pls post the official explanation for this question......thnks
Here's the OE from MGMAT -- pretty much along the same lines
of discussion here
The question asks us to find the slope of the line that goes through the origin and is equidistant from the two points P=(1, 11) and Q=(7, 7). It's given that the origin is one point on the requested line, so if we can find another point known to be on the line we can calculate its slope. Incredibly the midpoint of the line segment between P and Q is also on the requested line, so all we have to do is calculate the midpoint between P and Q! (This proof is given below).
Let's call R the midpoint of the line segment between P and Q. R's coordinates will just be the respective average of P's and Q's coordinates. Therefore R's x-coordinate equals 4 , the average of 1 and 7. Its y-coordinate equals 9, the average of 11 and 7. So R=(4, 9).
Finally, the slope from the (0, 0) to (4, 9) equals 9/4, which equals 2.25 in decimal form.
Proof
To show that the midpoint R is on the line through the origin that's equidistant from two points P and Q, draw a line segment from P to Q and mark R at its midpoint. Since R is the midpoint then PR = RQ.
Now draw a line L that goes through the origin and R. Finally draw a perpendicular from each of P and Q to the line L. The two triangles so formed are congruent, since they have three equal angles and PR equals RQ. Since the triangles are congruent their perpendicular distances to the line are equal, so line L is equidistant from P and Q.
