Question

reflects about a line such that N is the reflection of B and O is the reflection of C. Point N is shown on the coordinate plane, but point O is not.

The coordinates of point O are ( , )

Answer 1

The coordinates of O are (6,5).

Answer 2

Answer with explanation:

Coordinates of Point, B is (3,7),and Coordinates of point C is, (6,7).

Now, point B and C are reflected through a line to get , point N and Point O.

While reflection distance of point from Preimage is equal to distance of point from Image.

Line, y=6,is the Line of reflection.

Perpendicular Distance of point , N from Line , y=6 is 1 Unit.

So,Perpendicular, Distance from Point B , to Line, y=6,is equal to 1 Unit.

Similarly, Perpendicular Distance of point , C as well as point O, from Line , y=6 is 1 Unit.

Let , Coordinates of point , N be (x,y) and ,Coordinates of point , O be (p,q).

Joining, BN, Mid point of ,Segment, BN=(3,6)

Mid point of, Segment, CO=(6,6)

Using mid point formula

$x=\frac{x_{1}+x_{2}}{2},y=\frac{y_{1}+y_{2}}{2}\\\\ 3=\frac{x+3}{2}\\\\x+3=6\\\\x=6-3\\\\x=3\\\\ 6=\frac{y+7}{2}\\\\ y+7=12\\\\y=12-7\\\\y=5\\\\\frac{p+6}{2}=6\\\\ p+6=12\\\\p=12-6\\\\ p=6\\\\\frac{q+7}{2}=6\\\\q+7=12\\\\q=12-7\\\\q=5$

Coordinates of N=(3,5)

Coordinates of O=(6,5)