Triangle ABC is rotated to form △A'B'C' .The coordinates of point A are (1, 1) , the coordinates of point B are (3, 1) , and the coordinates of point C are (1, 4) .Which counter clockwise rotation around the origin results in the transformation of △ABC to △A'B'C' ?

Step-by-step explanation:

As we know the coordinate of point A = (1,1) , B = (3,1) and C = (1,4).

Rotate triangle ABC around the origin;

The rule for this transformation is:  (x,y) => (-y ,x)

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

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

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form