Question

question 7
a point has the coordinates (0, k). which reflection of the point will produce an image at the same coordinates, (0, k)?
a. a reflection of the point across the x - axis
b. a reflection of the point across the y - axis
c. a reflection of the point across the line y = x
d. a reflection of the point across the line y = -x

Explanation:

Step1: Recall reflection rules

For a point $(x,y)$: reflection across $x -$axis gives $(x,-y)$; across $y -$axis gives $(-x,y)$; across $y = x$ gives $(y,x)$; across $y=-x$ gives $(-y,-x)$.

Step2: Analyze reflection of point $(0,k)$

For point $(0,k)$:

• Reflection across $x -$axis: $(0,-k)$.
• Reflection across $y -$axis: $(0,k)$ (since $x = 0$, $-x=0$).
• Reflection across $y = x$: $(k,0)$.
• Reflection across $y=-x$: $(-k,0)$.

Answer:

B. a reflection of the point across the y - axis