Question

1. a triangle with vertices at j(-2,-5), k(-4,-1), and l(-1,-1) is rotated 90 counterclockwise about the origin, then reflected across the y - axis, and finally translated by the rule (x,y)→(x + 3,y + 4). what are the coordinates of the final image of vertex j?

. a) j(1,2)
. b) j(2,1)
. c) j(5,2)
. d) j(-2,2)
o a) j(1,2)
o b) j(2,1)
o c) j(5,2)
o d) j(-2,2)

Explanation:

Step1: Apply 90 - counterclockwise rotation rule

The rule for a 90 - counterclockwise rotation about the origin is $(x,y)\to(-y,x)$. For point $J(-2,-5)$, we have $(-(-5), - 2)=(5,-2)$.

Step2: Apply reflection across y - axis rule

The rule for reflecting a point $(x,y)$ across the y - axis is $(x,y)\to(-x,y)$. So for the point $(5,-2)$, we get $(-5,-2)$.

Step3: Apply translation rule

The translation rule is $(x,y)\to(x + 3,y+4)$. For the point $(-5,-2)$, we calculate $x=-5+3=-2$ and $y=-2 + 4=2$. So the final point is $(-2,2)$.

Answer:

D. $J'''(-2,2)$