Write an equation of a line that is perpendicular to the line x - 4y = 12 and passes through the point (2,3)

y = - 4x + 11

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

x - 4y = 12 ( subtract x from both sides )

- 4y = - x + 12 ( divide terms by - 4 )

y = x - 3 ← in slope- intercept form

with slope m =

Given a line with slope m then the slope of a line perpendicular to it is

= - = - = - 4 , then

y = - 4x + c ← is the partial equation

To find c substitute 2, 3 ) into the partial equation

3 = - 8 + c ⇒ c = 3 + 8 = 11

y = - 4x + 11 ← equation of perpendicular line

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source:

5104.38 inches

step-by-step explanation: