SOLUTION: reflect (4,-4) over y=3/4x-2

Algebra ->  Points-lines-and-rays -> SOLUTION: reflect (4,-4) over y=3/4x-2      Log On


   

Question 1053446: reflect (4,-4) over y=3/4x-2
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
any line perpendicular to the line
+y+=+%283%2F4%29%2Ax+-+2+ will have slope=
+-1%2Fm+=+-1%2F%283%2F4%29+
+-1%2Fm+=+-4%2F3+
------------------
The equation of the line through (4,-4)
and perpendicular to the given line is:
+%28+y+-+%28-4%29+%29+%2F+%28+x+-+4+%29+=+-4%2F3+
+y+%2B+4+=+%28-4%2F3%29%2A%28+x+-+4+%29+
+y+=+%28-4%2F3%29%2Ax+%2B+16%2F3+-+4+
+y+=+%28-4%2F3%29%2Ax+%2B+4%2F3+
-----------------------------
Find the point of intersection of the 2 lines
+%283%2F4%29%2Ax+-+2+=+%28-4%2F3%29%2Ax+%2B+4%2F3+
Multiply both sides by +12+
+9x+-+24+=+-16x+%2B+16+
+25x+=+40+
+x+=+8%2F5+
---------------
Plug this result back into the original equation
+y+=+%283%2F4%29%2Ax+-+2+
+y+=+%283%2F4%29%2A%288%2F5%29+-+10%2F5+
+y+=+6%2F5+-+10%2F5+
+y+=+-4%2F5+
The intersection is at ( 8/5, -4/5 )
Make this the midpoint of the reflected points
+%28+x+%2B+4+%29+%2F+2+=+8%2F5+
+5%2A%28+x+%2B+4+%29+=+2%2A8+
+5x+%2B+20+=+16+
+5x+=+-4+
+x+=+-4%2F5+
and
+%28+y+%2B%28-4%29+%29+%2F+2+=+-4%2F5+
+%28+y+-+4+%29+%2F+2+=+-4%2F5+
+5%2A%28+y+-+4+%29+=+-8+
+5y+-+20+=+-8+
+5y+=+12+
+y+=+12%2F5+
------------------
The reflected point is ( -4/5, 12/5 )
-----------------------------------
Here's the plot of the 2 lines:

Looks like my answer can be correct