Equation under rotation?

Question

The line y = 2x + 3 is rotated 90 deg about the origin. What is eqn of the rotated line

Answer 1

y = 2x + 3 rotated 90° anticlockwise is x = -2y - 3

This rearranges and simplifies to y = -1/2 x - 3/2



NOTE: 90° clockwise and 90° counterclockwise ARE NOT the same line! The other is y = -1/2 x + 3/2



Graph: https://www.desmos.com/calculator/ohpfwxgodw

Answer 2

A point (a,b) under a counter clock 90 deg is mapped to ( -b, a)



Now a point on the given (x, 2x+3) will be mapped to ( -2x - 3 , x)



Let (x',y') be on the rotated line

the y' =x and x' = -2x-3 or x = (x'+3)/-2

or y' = (x'+3)/-2

y' = -x'/2 - 3/2



So the eqn of the rotated line is y = -x/2 - 3/2

Answer 3

It is best to draw a diagram to visualize this.

y = 2x + 3 has y intercept at y = 3

and x intercept at x = -3/2

When you rotate the entire line about the origen by 90 degrees, the two

intercept are interchanged.

For the rotated line the y intercept is 3/2 and the x intercept is 3.

This is easy to see by looking at the diagram. I haven't done

it analytically.

The rotated line has equation

y = (-1/2)x + 3/2

Answer 4

Rotating 90° means the lines are perpendicular. (90° clockwise and 90° counterclockwise is the same line!)



y = (-1/2)x + 3