Answer
Below
Work Step by Step
To graph the line let us use the following table:
x = -2 y = -2 (-2, -2)
x = -1 y = -1 (-1, -1)
x = 0 y = 0 (0, 0)
x = 1 y = 1 (1, 1)
x = 2 y = 2 (2, 2)
To graph the line joining the points (a, b) and (b, a) use the following table:
a = 1 b = 2 (1, 2)
a = 2 b = 1 (2, 1)
a = 0 b = 3 (0, 3)
a = 3 b = 0 (3, 0)
The midpoint of (1, 2) and (2, 1) is
$ M (x, y) = M((1+2)/2 , (2+1)/2 )$
$= M( 3/2 , 3/2 ) $
M(1.5, 1.5) lies on the line y = x.
The slope of y = x is,
$ m₁ = 1 $
The slope of the line joining the points (1, 2) and (2, 1) is:
$ m₂ = (y_2-y_1)/(x_2-x_1 )$
$ = (1-2)/(2-1) $
$= (-1)/1$
$ = -1$
$m₁× m₂ = 1 × - 1 = -1$
This shows that the two lines are perpendicular to each other.
