Answer:
Option C is correct.
Explanation:
Slope of line JK
J (1,-6) K (0,4)
slope of JK = y₂ - y₁ / x₂ - x₁
Slope of JK = 4-1/0-(-6) = 3/6 = 1/2
so slope of JK = 1/2
Slope of line LM
L (-5,-3) and M(0,3)
slope of LM = y₂ - y₁ / x₂ - x₁
slope of LM = 3-(-5)/0-(-3) = 3+5/3 = 8/3
Slope of line NO
N(-6,-5) and 0 (0,0)
slope of NO = y₂ - y₁ / x₂ - x₁
slope of NO = 0-(-6)/0-(-5) = 6/5
So, slope of line NO = 6/5
Slope of PQ
P(-5,4) Q(0,-2)
slope of PQ = y₂ - y₁ / x₂ - x₁
slope of PQ = -2-4/0-(-5) = -2/5
so slope of line PQ = -2/5
the two lines are perpendicular if slope of one line is m then slope of other line is -1/m
The slope of given line =m= -5/6
The slope of line perpendicular to the given line = -1/m = 6/5
So, line NO is perpendicular to the given line as its slope is 6/5
Option C is correct.