Question

graph the image of (j(1, - 4)) after a rotation (90^{circ}) counterclockwise around the origin.

Explanation:

Step1: Recall rotation rule

The rule for a 90 - degree counter - clockwise rotation around the origin is $(x,y)\to(-y,x)$.

Step2: Apply rule to point J

Given $J(1,-4)$, substitute $x = 1$ and $y=-4$ into the rule. We get $(-(-4),1)$.

Step3: Simplify coordinates

$-(-4)=4$, so the new coordinates are $(4,1)$.

Answer:

The image of $J(1,-4)$ after a 90 - degree counter - clockwise rotation around the origin is $(4,1)$.