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

reflection in the y- axis

Step-by-step explanation:

The point (0, k ) lies on the y- axis

Thus a reflection of the point in the y- axis means the point is invariant, that is remains unchanged.

 the correct option is

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

Step-by-step explanation:  Given that a point has co-ordinates (0, k).

We are to select the correct reflection of the point that will produce an image at the same coordinates, (0, k)

(A) If a point (a, b) is reflected across the X-axis, then the sign before its y co-ordinate changes. That is, (a, b) reflects to (a, -b).

So, (0, k) will become (0, -k).

So, first option is not correct.

(B) If a point (a, b) is reflected across the Y-axis, then the sign before its x co-ordinate changes. That is, (a, b) reflects to (-a, b).

So, (0, k) will become (0, k).

So, second option is CORRECT.

(C) If a point (a, b) is reflected across the line y = x, then its co-ordinates becomes (-b, -a).

So, (0, k) will become (-k, 0).

So, third option is not correct.

(D) If a point (a, b) is reflected across the line y = -x, then its co-ordinates becomes (b, -a).

So, (0, k) will become (k, 0).

So, fourth option is not correct.

Thus, (B) is the correct option.

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet