Question 124921
TO ANSWER THIS PROBLEM WE NEED TO FIND THE SLOPES OF THESE 2 LINES THUS:
Y=mX+b WHHERE m=SLOPE.
X-2Y=10 OR -2Y=-X+10 OR Y=-X/-2+10/-2 OR Y=X/2-5 (RED LINE)WHICH GIVES US A SLOPE=1/2.
2X+Y=2 OR Y=-2X+2 (GREEN LINE) WHICH GIVES US A SLOPE=-2. 
SEEING AS THESE 2 SLOPES (1/2 & -2) ARE NEGATIVE RECIPRICALS OF EACH OTHER THEN THESE 2 LINES ARE PERPENDICULAR TO ONE ANOTHER.
PROOF:
{{{ graph( 300, 300, -10, 10, -10, 10, y = x/2 -5, y = -2x +2) }}} (graph 300x300 pixels, x from -10 to 10, y from -10 to 10, of TWO functions y = x/2 -5 and y = -2x +2).