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?

 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).

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'

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

so, we will get reflected point as

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

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

step-by-step explanation:

what is the figure? attach a picture.