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B is the midpoint of AC and E' is the midpoint of BD. If A(-9,-4), C(-1, 6), and E(-4,-3), find the coordinates of D.

Respuesta :

MrGumby
The coordinates for D are (-4, -7)

First we must locate point B as it is vital to finding the midpoint of BD. To do this, we take the average of the endpoints AC since B is its midpoint. 

x values = -9 + 1 = -8
Then divide by 2 for the average -8/2 = -4

y values = -4 + 6 = 2
Then divide by 2 for the average 2/2 = 1

Therefore B must be (-4, 1)

Now we know the values of E must be the average of B and D. So we can write equations for each coordinate since we know they are averages. 

x - values = (Bx + Dx)/2 = Ex
(-4 + Dx)/2 = -4 ---> multiply both sides by 2
-4 + Dx = -8 ---> add -4 to both sides
Dx = -4

y - values = (By + Dy)/2 = Ey
(1 + Dy)/2 = -3 ---> multiply both sides by 2
1 + Dy = -6 ---> subtract 1 from both side
Dy = -7

So the coordinates for D must be (-4, -7)

Answer:

The coordinates of D are:

                   (-3,-7)

Step-by-step explanation:

We know that if a point B(c,d) is located in middle of two points i.e. A(a,b) and C(a',b').

Then the coordinates of B is given by:

[tex]c=\dfrac{a+a'}{2}\ and\ d=\dfrac{b+b'}{2}[/tex]

It is given that:

B is the midpoint of AC.

A(-9,-4), C(-1, 6).

Hence, the coordinates of B(x,y) is given by:

[tex]x=\dfrac{-9-1}{2}\ and\ y=\dfrac{-4+6}{2}\\\\x=\dfrac{-10}{2}\ and\ y=\dfrac{2}{2}\\\\x=-5\ and\ y=1[/tex]

i.e. the coordinates of B are: (-5,1).

E is the midpoint of BD.

Let the coordinates of D be (w,z)

Also, E is located at E(-4,-3).

i.e.

[tex]-4=\dfrac{-5+w}{2}\ \ and\ \ -3=\dfrac{1+z}{2}\\\\-4\times 2=-5+w\ \ and\ \ -3\times 2=1+z\\\\-8=-5+w\ \ and\ \ -6=1+z\\\\w=-8+5\ \ and\ \ z=-6-1\\\\w=-3\ \ and\ \ z=-7[/tex]

Hence, the coordinates of D are: (-3,-7)

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