Answer: Point C is (0, -7)
Step-by-step explanation:
For a general line y = a*x +b
A perpendicular line to this one will have a slope equal to -(1/a)
First, for a line y = a*x + b that passes through points (x₁, y₁) and (x₂, y₂) the slope is:
a = (y₂ - y₁)/(x₂ - x₁)
Then for a line that passes through the points A (-4, 5) and B (5, 8) the slope is:
a = (8 - 5)/(5 - (-4)) = 3/9 = 1/3
a = 1/3
Then, a line perpendicular to this one will have the slope:
a' = -(1/(1/3) = -3
Then the perpendicular line is something like:
y = -3*x + b
Now we know that this line passes through point A, then when x = -4, we have y = 5
if we replace these values we get:
5 = -3*(-4) + b
5 = 12 + b
5 - 12 = b
-7 = b
Then our line is:
y = -3*x - 7
This line intersects the y-axis at point C, we know that the y-axis corresponds to x = 0.
Then:
y = -3*0 - 7
y = -7
The point C is (0, -7)
