Question

1. triangle abc with a(1,1) b(2,4) c(3,1) is rotated 90° counterclockwise about the origin, then reflected across the x-axis. what are the coordinates of the image? a(-1,1) b(-4,2) c(-1,3)

Explanation:

Step1: 90° CCW rotation rule

For a point $(x,y)$, rotating 90° counterclockwise about the origin transforms it to $(-y,x)$.

Step2: Rotate point A(1,1)

$A' = (-1, 1)$

Step3: Rotate point B(2,4)

$B' = (-4, 2)$

Step4: Rotate point C(3,1)

$C' = (-1, 3)$

Step5: Reflect over x-axis rule

For a point $(x,y)$, reflecting across the x-axis transforms it to $(x,-y)$.

Step6: Reflect rotated A'(-1,1)

$A'' = (-1, -1)$

Step7: Reflect rotated B'(-4,2)

$B'' = (-4, -2)$

Step8: Reflect rotated C'(-1,3)

$C'' = (-1, -3)$

Answer:

The coordinates of the image are $A(-1,-1)$, $B(-4,-2)$, $C(-1,-3)$