SOLUTION: Line m passes through points (-4, 3) and (2, -6). If line q is generated by reflecting m across the line y=x, then which of the following represents the equation of q? a. 3x + 2

Question 1127490: Line m passes through points (-4, 3) and (2, -6). If line q is generated by reflecting m across the line y=x, then which of the following represents the equation of q?
a. 3x + 2y = 6
b. 2x + 3y = -6
c. 2x + 3y = 6
d. -2x + 3y = 6
e. 3x + 2y = 18
Found 2 solutions by htmentor, greenestamps:
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
When you reflect any point about the line y=x, the x and y coordinates get swapped. The equation for the line m is:
y - 3 = (3 - -6)/(-4 - 2)(x + 4)
y - 3 = (-3/2)(x + 4)
y - 3 = (-3/2)x - 6
y = (-3/2)x - 3
3x + 2y = -6
Thus the equation for the reflected line is:
2x + 3y = -6
Ans: b
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The basic idea is, as the other tutor said, that when you reflect a line (or any graph) over the line y=x, the x and y coordinates get switched.

His method for solving the problem was to find the equation of the line through the two given points and switch the x and y in the equation.

Another method would to be to switch the coordinates of the two given points and find the equation of the line through those two points:

The two reflected points are (3,-4) and (-6,2).
The slope of the line through those two points is -6/9 = -2/3.
Using either of the two points and the slope, the equation of the line is y = (-2/3)x-2.
Changing the equation to standard form gives 2x+3y=6.

Both methods are equally valid, and equally easy. If you have several problems like this, try both methods and find which you find easier to use.
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