Perpendicular Bisector Problem

[mithra]

I came across this problem in MGMAT CAT:

Q) In the xy-coordinate system, what is the slope of the line that goes through the origin and is equidistant from the two points P = (1, 11) and Q = (7, 7)?

and the correct answer was 2.25 which was solved by MGMAT by finding the mid-point and then finding the slope with mid-point and (0,0) as coordinated.

I did not understand the proof given, to prove R is mid point on line:
"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."

Does it mean it is a perpendicular bisector to line segment PQ, then can't we find the slope of PQ and then take the negetive reciprocal for the perpendicular bisector?

Thanks.

[amitganguly2k12]

[quote="mithra"]I came across this problem in MGMAT CAT:

Q) In the xy-coordinate system, what is the slope of the line that goes through the origin and is equidistant from the two points P = (1, 11) and Q = (7, 7)?

and the correct answer was 2.25 which was solved by MGMAT by finding the mid-point and then finding the slope with mid-point and (0,0) as coordinated.

I did not understand the proof given, to prove R is mid point on line:


explanation-regarding-lines-t8389.html please refer this.

[Ben Ku]

Please disregard this problem. It is flawed, and has been taken out of our CAT pool to be rewritten. Refer to the following post.

explanation-regarding-lines-t8389.html