Question

question 1
△abc has vertices (-3, 4), (-7, 8), and (-5, 2).
△abc is reflected over the x - axis and then translated two units up and three units left.
which of the coordinates is not a vertex of △abc?
(-3, -4)
(-10, -6)
(-6, -2)
(-6, 0)
question 2
quadrilateral wxyz has vertices w(1, 1), x(3, 1), y(1, 3), z(3, 3).
it was rotated 180° clockwise and reflected over the line x = 0.
which coordinate would be the correct coordinate pair for y?
(-3, 1)
(3, -1)
(-1, -3)
(1, -3)

Explanation:

Step1: Reflect $\triangle ABC$ over x - axis

The rule for reflecting a point $(x,y)$ over the $x$-axis is $(x,-y)$.
For vertex $(-3,4)$: $( - 3,-4)$; for $(-7,8)$: $(-7,-8)$; for $(-5,2)$: $(-5,-2)$.

Step2: Translate the reflected points

The rule for translating a point $(x,y)$ two units up and three units left is $(x - 3,y + 2)$.
For $(-3,-4)$: $(-3-3,-4 + 2)=(-6,-2)$; for $(-7,-8)$: $(-7-3,-8 + 2)=(-10,-6)$; for $(-5,-2)$: $(-5-3,-2 + 2)=(-8,0)$.
The vertices of $\triangle A''B''C''$ are $(-6,-2),(-10,-6),(-8,0)$. So the point $(-3,-4)$ is not a vertex of $\triangle A''B''C''$.

For the second question:

Step1: Rotate quadrilateral $WXYZ$ 180° clockwise

The rule for rotating a point $(x,y)$ 180° clockwise about the origin is $(-x,-y)$.
For vertex $Y(1,3)$: $(-1,-3)$.

Step2: Reflect the rotated point over the line $x = 0$

The rule for reflecting a point $(x,y)$ over the line $x = 0$ (the $y$-axis) is $(-x,y)$.
For $(-1,-3)$: $(1,-3)$.

Answer:

Question 1: A. $(-3,-4)$
Question 2: D. $(1,-3)$