Question

the coordinates of the vertices of CDE are C(1,4), D(3,6), and E(7,4). if the triangle is reflected over the line y=3, what are the coordinates of the image of d?

Answer 1

we are given vertices of CDE as

C(1,4), D(3,6), and E(7,4)

It is reflected about y=3 line

Let's assume reflected point as D'

D'=(a,b)

Mid-point will be at y=3

so, M=(3,3)

so, M is the mid-point of D and D'

$(3,3)=(\frac{3+a}{2}, \frac{6+b}{2})$

now, we can solve for 'a' and 'b'

$3=\frac{3+a}{2}$

$3+a=6$

$a=3$

$3=\frac{6+b}{2}$

$6=6+b$

$b=0$

so, we will get reflected point as

D'=(3,0)...........Answer

Answer 2

Answer:  The required co-ordinates of the image of D are (3, 0).

Step-by-step explanation:  Given that the co-ordinates of the vertices of triangle CDE are C(1,4), D(3,6), and E(7,4). The triangle CDE is reflected over the line y=3.

We are to find the co-ordinates of the image of vertex D.

We know that

if a point with co-ordinates (x, y) is reflected across the line y = k, then the co-ordinates changes according to the following rule :

(x, y)    ⇒      (x, 2k - y).

So, the co-ordinates of the image of vertex D after reflection from the line y = 3 is

D(3, 6)    ⇒     D'(3, 2 × 3 - 6) = D'(3, 0).

The reflection is shown in the attached figure below.

Thus, the required co-ordinates of the image of D are (3, 0).