Line DE contains the points D (–1, –4) and E (3, 3). Line FG contains the point F (–3, 3). Which set of coordinates for point G makes the two lines perpendicular?

The set of coordinates for point G that make the two lines perpendicular are given through the relation

7y = -4x + 9

Step-by-step 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!!!

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.