On a coordinate plane, line A B goes through (negative 2, 4) and (0, negative 4). Point Z is at (0, 2). Which point is on the line that passes through point Z and is perpendicular to line AB?On a coordinate plane, line A B goes through (negative 2, 4) and (0, negative 4). Point Z is at (0, 2).
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)

(–4, 1)  

Step-by-step explanation:

1. Calculate the slope of AB

m₁ = (y₂ - y₁)/(x₂ - x₁) = (-4 - 4)/(0 -(-2))= -8/2 = -4

2. Calculate the slope of the perpendicular line

m₂ = -m₁ = ¼

3. Calculate its y-intercept

Point Z, (0,2), is the y-intercept.

4. Write the equation for the line

Insert the values of m and b

y = ¼x + 2

5. Check the points

(a) (-4,1)

1 = ¼(-4)+ 2

1 = -1 + 2

1 = 1

TRUE

(b) (1,-2)

-2 = ¼(1) + 2

-2 = ¼ + 2

-2 = 2¼

FALSE

(c) (2,0)

0 = ¼(2) + 2

0 = ½ + 2

0 = 2½

FALSE

(d)  

4 = ¼(4) + 2

4 = 1 + 2

4 = 3

FALSE

Only (-4,1) is on the perpendicular line.

The diagram shows the line going through AB in red and the perpendicular line in purple.

1. 3

2. 4

3. 1

hope this ! have a great day.

-wfz