Answer:
The set of coordinates for point G that make the two lines perpendicular are given through the relation
7y = -4x + 9
Explanation:
The condition for perpendicularly of two lines is that the products of the slope of the two lines, m₁ and m₂ must be equal to -1.
For a line whose two points (x₁, y₁) and (x₂, y₂)
on the line are known, the slope of the line, m, is given as
m = (Δy/Δx) = (y₁ - y₂) ÷ (x₁ - x₂)
points D (–1, –4) and E (3, 3).
Let the slope of DE be m₁ and the slope of FG be m₂
Since the two lines are perpendicular,
m₁m₂ = -1
m₁ = (Δy/Δx) = (-4 - 3) ÷ (-1 -3) = (7/4) = 1.75
Since, m₁m₂ = -1, this means that,
m₂ = (-1/m₁) = (-1/1.75) = -(4/7)
Let the coordinates of point G be (x, y)
m₂ = (3 - y) ÷ (-3 - x)
(-4/7) = [(3-y)/(-3-x)]
-4(-3-x) = 7(3-y)
12 + 4x = 21 - 7y
7y = -4x + 9
Hope this Helps!!!