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PSAT math problem

DusterbugDusterbug - Posts: 391 Member
edited August 2011 in SAT Preparation
This is from the 2010 Wednesday PSAT.

18. In the xy-plane, the two points A (-2,-5) and B (3,2) are each reflected about the line y=x. What is the slope of the line containing the points to which A and B are reflected?

A. -7/5

B. -5/7

C. 1/7

D. 5/7

E. 7/5

The answer is D, and I cannot figure out why for the life of me.
Post edited by Dusterbug on

Replies to: PSAT math problem

  • limabeans01limabeans01 Registered User Posts: 619 Member
    a reflection over the y=x line is the inverse. Just switch the x and y coordinates and find the new slope (e.g. use (-5,-2)and(2,3)
  • IceQubeIceQube Registered User Posts: 3,187 Senior Member
    ^Beat me to it. In general, a reflection over the line y=x means:

    (X,Y) -> (Y, X).

    In this case:

    (3,2) -> (2, 3)
    (-2,-5) -> (-5,-2)


    -2-3 = -5 (change in y)

    -5-2 = -7 (change in x)

    -5/-7 = 5/7 = Answer Choice D.
  • whodareswinswhodareswins Registered User Posts: 349 Member
    Problem from the recent PSAT I suppose?
  • IceQubeIceQube Registered User Posts: 3,187 Senior Member
    ^Yes. 10char.
    Dusterbug wrote:
    This is from the 2010 Wednesday PSAT.
  • Aceventura74Aceventura74 Registered User Posts: 187 Junior Member

    IceQube nailed the answer dead on. First you want to (if need be) just sketch the points and the line y=x. Then realize the translation formula switches the (x,y) coordinates. Finally, the slope formula is Delta y/delta x, meaning (y2-y1)/(x2-x1).

  • DusterbugDusterbug - Posts: 391 Member
    All right thanks everybody, I knew there was something specific I was supposed to be doing to solve this. I don't think I ever actually learned that reflections invert the x,y coordinates. glad I learned that now
  • Aceventura74Aceventura74 Registered User Posts: 187 Junior Member

    If you can't remember an exact translation formula, you can always sketch it out. Physically draw it on a scrap grid and think about a reflection. That always helped me before I learned my rules.

  • DrSteveDrSteve Registered User Posts: 1,288 Senior Member

    Reflections in general don't interchange the x and y values. The SPECIFIC reflection in the line y=x does this.

    A reflection in the y-axis negates the x-coordinate.
    A reflection in the x-axis negates the y-coordinate.

    Although it's worth memorizing these, keep in mind that if you forget you can just draw a picture.
This discussion has been closed.