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)
Answer:
B
Step-by-step explanation:
We can figure out the initial value and base of an exponential function if the function is written in the form where
a is the initial value, and
b is the base
<u>Note:</u> a ≠ 0 and b ≠ 1
Our equation given can be written in this form by writing it like
Thus, this is an <em>exponential function</em>. The initial value is 1 and the base is 5.
The correct answer is B
Answer:
125
Step-by-step explanation:
A is an inscribed angle. The central angle is 90, so angle A is 45.
110/2 = 55
180 - 45 - 55 = 80
Angle B is 80.
80 + 45 = 125
Answer:
J' = (3,0)
K' = (3,-2)
L' = (0,-2)
Step-by-step explanation: