We have been given two points on each line, so we have enough information to calculate their slopes using the Slope Formula.
m=y_2- y_1/x_2- x_1
Note that when choosing points to substitute for ( x_1, y_1) and ( x_2, y_2), it does not matter which points on the line you choose, since the result will be the same. Let's start with line l_1, which passes through ( -2, 4) and ( 2, 0).
The slope of line l_1 is -1 We will use the same method to identify the slope of line l_2.
Line
Points
y_2-y_1/x_2-x_1
Slope
l_1
( -2, 4) & ( 2, 0)
0- 4/2-( -2)
-1
l_2
( 3, 4) & ( -3, -2)
-2- 4/-3- 3
1
To determine whether or not the lines are perpendicular, we calculate the product of their slopes. Any two slopes whose product equals -1 are negative reciprocals, and therefore the lines are perpendicular.
-1(1)=-1
We have found that lines l_1 and l_2 are perpendicular to one another.
