Question

1. triangle pqr has vertices p(0,0), q(-2,3), and r(-4,1). it is reflected across the y - axis, rotated 270 degrees counterclockwise about the origin, and then translated by (x,y)→(x - 2,y + 4). what are the coordinates of vertex q?

a) (1,2)
b) (-5,6)
c) (1,6)
d) (-1,2)

Explanation:

Step1: Reflect Q across y - axis

When reflecting a point $(x,y)$ across the $y$-axis, the transformation is $(x,y)\to(-x,y)$. For point $Q(-2,3)$, after reflection across the $y$-axis, the new point $Q_1$ is $(2,3)$.

Step2: Rotate $Q_1$ 270 degrees counter - clockwise about the origin

A 270 - degree counter - clockwise rotation about the origin has the transformation $(x,y)\to(y, - x)$. For point $Q_1(2,3)$, after rotation, the new point $Q_2$ is $(3,-2)$.

Step3: Translate $Q_2$

The translation rule is $(x,y)\to(x - 2,y + 4)$. For point $Q_2(3,-2)$, we have $x=3$ and $y = - 2$. After translation, $x'=3-2=1$ and $y'=-2 + 4=2$. So the final point is $(1,2)$.

Answer:

A. $(1,2)$