Assume P(xp,yp), A(xa,ya), etc. We know that rotation rule of 90<span>° clockwise about the origin is R_-90(x,y) -> (y,-x) For example, rotating A about the origin 90</span><span>° clockwise is (xa,ya) -> (ya, -xa) or for a point at H(5,2), after rotation, H'(2,-5), etc.
To rotate about P, we need to translate the point to the origin, rotate, then translate back. The rule for translation is T_(dx,dy) (x,y) -> (x+dx, y+dy)
So with the translation set at the coordinates of P, and combining the rotation with the translations, the complete rule is: T_(xp,yp) R_(-90) T_(-xp,-yp) (x,y) -> </span>T_(xp,yp) R_(-90) (x-xp, y-yp) -> T_(xp,yp) (y-yp, -(x-xp)) -> (y-yp+xp, -x+xp+yp)
Example: rotate point A(7,3) about point P(4,2) => x=7, y=3, xp=4, yp=2 => A'(3-2+4, -7+4+2) => A'(5,-1)
Alright, so in order to solve this, we need to isolate the variable. So, we need to simplify the equation. So, we have the equation: 82•P = 84 So, we need to divide both sides by 82 because it is the opposite of multiplication. So, we have : 82•P/82 = 84/82 So, 82•P/82 = 1p = P. 84/82 = P If You Need Decimal Form, 84/82 = About 1.02
