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!!!

answer: e 9, 5.75

step-by-step explanation:

step 1

find the variation ab in the x coordinate

delta x=(x2-x1)=10-> 8 units

find the variation ab  in the y coordinate 

delta y=(y2-y1)=6-> 2 units

step 2

find the coordinates point c

  x coordinate 

cx=ax+delta x*2/> cx=2+8*(2/> cx=3

  y coordinate 

cy=ay+delta y*2/> cy=4+2*(2/> cy=4.25

the coordinates of point c are (3,4.25)

step 3

find the coordinates point d

  x  coordinate 

dx=ax+delta x*4/> dx=2+8*(4/> dx=4

  y  coordinate 

dy=ay+delta y*4/> dy=4+2*(4/> dy=4.5

the coordinates of point d are (4, 4.5)

step 4

find the coordinates point e

  x  coordinate 

ex=ax+delta x*4/> ex=2+8*(6/> ex=5

  y  coordinate 

ey=ay+delta y*4/> ey=4+2*(6/> ey=4.75

the coordinates of point e are (5, 4.75)

step 5

find the coordinates point f

  x  coordinate 

fx=ax+delta x*4/> fx=2+8*(8/> fx=6

  y  coordinate 

fy=ay+delta y*4/> fy=4+2*(8/> fy=5

the coordinates of point f are (6,5)

step 6

find the coordinates point g

  x  coordinate 

gx=ax+delta x*4/> gx=2+8*(10/> gx=7

  y  coordinate 

gy=ay+delta y*4/> gy=4+2*(10/> gy=5.25

the coordinates of point g are (7,5.25)

step 7

find the coordinates point h

  x  coordinate 

hx=ax+delta x*4/> hx=2+8*(12/> hx=8

  y  coordinate 

hy=ay+delta y*4/> hy=4+2*(12/> hy=5.5

the coordinates of point h are (8,5.5)

step 8

find the coordinates point i

  x  coordinate 

ix=ax+delta x*4/> ix=2+8*(14/> ix=9

  y  coordinate 

iy=ay+delta y*4/> iy=4+2*(14/> iy=5.75

the coordinates of point i are (9,5.75)

- r3ktforgood ☕