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

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).

Answer 2

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)=((3+a)/(2), (6+b)/(2))`

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

`3=(3+a)/(2)`

`3+a=6`

`a=3`

`3=(6+b)/(2)`

`6=6+b`

`b=0`

so, we will get reflected point as

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