imgur(.)com/gallery/0gZRygN/new
link to quesion pic
- In the figure above, point P is the reflection of point A through the line y = x. What is the slope of the line that passes through points A and P ? (A) −1 (B) − 1 2 (C) 0 (D) 1 2 (E) 1
(A) -1.
Points reflected about the y=x line have a special property: their y’s and x’s are switched.
Algebraically:
if point A is (3,1) and is reflected about y=x, then point P is (1,3).
Now you have two points of the line with the slope you’re trying to find.
Using the slope formula with the two points above, you have m = 2/-2 = -1.
Logically:
If you’re reflecting a point across a particular line, the point and its reflected point would form a line perpendicular to the original line. y=x has a slope of 1; therefore, the new line has an opposite reciprocal slope, -1.