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# PSAT math problem

- Posts: 391 Member
edited August 2011
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

• 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)
• 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)

Slope:

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

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

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

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).

~Aceventura74
• - 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
• Registered User Posts: 187 Junior Member
Dusterbug,

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.

~Aceventura74
• Registered User Posts: 1,288 Senior Member
Dusterbug,

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.