For this case we have that if the line that passes through point z is perpendicular to line AB, it is fulfilled that:
[tex]m * m_ {AB} = - 1[/tex]
We find the slope of AB:
[tex]m_ {AB} = \frac {y2-y1} {x2-x1}[/tex]
We choose the points that go through AB:
(-2.4)
(0, -4)
[tex]m_ {AB} = \frac {-4-4} {0 - (- 2)}\\m_ {AB} = \frac {-8} {2}\\m_ {AB} = - 4[/tex]
So:
[tex]m * -4 = -1\\m = \frac {1} {4}[/tex]
On the other hand, the point z is (0,2).
Then the cut point with the "y" axis is 2.
The equation of the line is:
[tex]y = \frac {1} {4} x + 2[/tex]
We test the points:
(-4,1)
[tex]1 = \frac {1} {4} (- 4) +2\\1 = -1 + 2\\1 = 1[/tex]
Is fulfilled
(1, -2)
[tex]-2 = \frac {1} {4} (1) +2\\-2 = \frac {1} {4} +2[/tex]
It is not true
(2,0)
[tex]0 = \frac {1} {4} (2) +2[/tex]
It is not true
(4,4)
[tex]4 = \frac {1} {4} (4) +2\\4 = 1 + 2[/tex]
It is not true
Answer:
Option A
