If two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line. Recall, the formula for calculating slope is expressed as
slope = (y2 - y1)/(x2 - x1)
From the information given,
Considering L1,
x1 = 0, y1 = 3
x2 = 3, y2 = 1
Slope = (1 - 3)/(3 - 0)
Slope = - 2/3
Considering L2,
x1 = - 1, y1 = 4
x2 = - 7, y2 = - 5
Slope = (- 5 - 4)/(- 7 - - 1) = - 9/(- 7 + 1) = -9/- 6 = 9/6
Dividing the numerator and denominator by 3,
Slope = 3/2
We can see that - 2/3 is the negative reciprocal of 3/2. Thus, the lines created using the given points perpendicular