Question

Rotate the vector (3,-2) 90°
counter-clockwise about the
origin.

Answer 1

If the coordinate is (3, -2) then after the 90° counter-clockwise about the origin. Then new coordinate will be (2, 3).

What is coordinate geometry?

Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.

Convert the cartesian coordinate to the polar coordinate. Then we have

$r = \sqrt{3^2 + (-2)^2}\\\\r = \sqrt{9 + 4 }\\\\r = 3.61\\\\\theta = \tan ^{-1}\dfrac{-2}{3}\\\\\theta = -33.69^o\\\\\theta = 326.31^o$

Then 90° counter-clockwise about the origin, then the angle will be

θ = 326.31 + 90 = 431.31

But θ is from 0 to 360. Then

θ = 431.31 - 360 = 56.31

Then convert the polar coordinate to the cartesian coordinate. Then we have

x = r cosθ

x = 3.61 × cos 56.31

x = 2

and

y = r sinθ

y = 3.61 × sin 56.31

y = 3

More about the coordinate geometry link is given below.

https://brainly.com/question/1601567

#SPJ2