Which point is on the line that passes through point Z and is perpendicular to line AB? (–4, 1) (1, –2 ) (2, 0) (4, 4)

Question

asked Oct 5, 2020 123k views

2 Answers

Seyong Cho · Answer 1 · 2020-10-10T05:44:35+0000

For this case we have that if the line that passes through point z is perpendicular to line AB, it is fulfilled that:

$m * m_ {AB} = - 1$

We find the slope of AB:

$m_ {AB} = \frac {y2-y1} {x2-x1}$

We choose the points that go through AB:

(-2.4)

(0, -4)

$m_ {AB} = \frac {-4-4} {0 - (- 2)}\\m_ {AB} = \frac {-8} {2}\\m_ {AB} = - 4$

So:

$m * -4 = -1\\m = \frac {1} {4}$

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:

$y = \frac {1} {4} x + 2$

We test the points:

(-4,1)

$1 = \frac {1} {4} (- 4) +2\\1 = -1 + 2\\1 = 1$

Is fulfilled

(1, -2)

$-2 = \frac {1} {4} (1) +2\\-2 = \frac {1} {4} +2$

It is not true

(2,0)

$0 = \frac {1} {4} (2) +2$

It is not true

(4,4)

$4 = \frac {1} {4} (4) +2\\4 = 1 + 2$

It is not true

Answer:

Option A