Question

GEOMETRY!!!! K' (6,5) is the image of K after a reflection in the line y=2. what are the coordinates of K

Answer 1

Given:

The coordinates of point K' are (6,5).

K' is the image of K after a reflection in the line y=2.

To find:

The coordinates of point K.

Solution:

Let the coordinates of point K are (a,b).

If a figure is reflected over the line y=2, then

$(x,y)\to (x,2(2)-y)$

$(x,y)\to (x,4-y)$

Using this formula, the coordinates of image of K are

$K(a,b)\to K'(a,4-b)$

The coordinates of point K' are (6,5).

$K'(a,4-b)=K'(6,5)$

On comparing both sides, we get

$a=6\text{ and }4-b=5$

$a=6\text{ and }-b=5-4$

$a=6\text{ and }-b=1$

$a=6\text{ and }b=-1$

Therefore, the coordinates of point K are (6,-1).