On a coordinate plane, line A B goes through (negative 2, 4) and (0, negative 4). Point Z is at (0, 2).
2 answers:
Answer:
(–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.
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