Answer:
C. (-1, 0)
Step-by-step explanation:
You want the point of intersection of the line x+y+1 = 0 and the perpendicular line through (2, 3).
Perpendicular line
The equation of the perpendicular line can be written by swapping the x- and y-coordinates and negating one of them. The new constant must be chosen so the given point satisfies the equation.
Since both the coefficients are the same, equation of the perpendicular just has one of them negated. We like to have a positive leading coefficient, so we can write the equation as ...
x -y = 2 -3 = -1 . . . . . . . using (x, y) = (2, 3) to find the constant
x -y +1 = 0
Foot
Adding this equation to the given line's equation, we can eliminate the y-variable and find the x-coordinate of the foot point.
(x +y +1) +(x -y +1) = 0 +0
2x +2 = 0
x = -1 . . . . . . matches choice C
-1 +y +1 = 0 ⇒ y = 0 . . . . . . using the first line's equation
The coordinates of the point of intersection are (-1, 0), choice C.
