Question

6.) given bc with b(1, 4) and c(6, 1). determine the coordinates of b\c\ if bc is rotated 90° counterclockwise about the point p(-1, -2) and then translated down 5 units and right 1 unit. graph and list the coordinates of b\ and c\. 7.) given bc with b(1, 4) and c(6, 1). determine the coordinates of b\c\ if bc is rotated 180° about the origin and then reflected over the x - axis.

Explanation:

Step1: Rotate 90 - degree counter - clockwise about a point

The formula for rotating a point $(x,y)$ counter - clockwise 90 degrees about a point $(a,b)$ is $(a-(y - b),b+(x - a))$.
For point $B(1,4)$ about $P(-1,-2)$:
$x_1=-1-(4 + 2)=-7$
$y_1=-2+(1+1)=0$
For point $C(6,1)$ about $P(-1,-2)$:
$x_2=-1-(1 + 2)=-4$
$y_2=-2+(6 + 1)=5$

Step2: Translate the rotated points

The translation rule is $(x,y)\to(x + 1,y-5)$.
For the rotated $B$:
$x_3=-7 + 1=-6$
$y_3=0-5=-5$
For the rotated $C$:
$x_4=-4 + 1=-3$
$y_4=5-5=0$

Answer:

$B''(-6,-5)$, $C''(-3,0)$