Points A(-2, 4), B(1, 3), C(4, -1) and D form a parallelogram. What are the coordinates of D?

2 answers:

8 0

Let point A(-2,4) = A (X1,Y1)
point B( 1,3 )= B (X2,Y2)
point C(4,-1) = C (X3,Y3)
and point D(?, ?) = D (X4,Y4) We have to find this point

To find X4 we have to use the formula:
X2-X1=X3-X4

Now just plug in the numbers that correspond to the letters provided:
(1)-(-2)=(4)-(X4) ----> we don't know what X4 is yet, so we have to solve for it!
1+2=4-X4
3=4-X4
3-4=-X4
-1=-X4 divide both sides by -1
X4=1

Now we have to find Y4 using this formula:
Y2-Y1=Y3-Y4

Therefore,
(3)-(4)=(-1)-(Y4)
-1=-1-Y4
-1+1=-Y4
0=-Y4
So,
Y4=0

Now we have found the coordinates of the point D, which is (1,0)

Hope this helped!

Basile [38]3 years ago

3 0

Answer: d- (1,0)

Step-by-step explanation:

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xxTIMURxx [149]

Answer: A'=(1, 3); B'=(-3, 4);C'=(3, 0); D'=(-2, 5)

You can check the PNG attached as well.

Step-by-step explanation:

You need to represent the symmetry of every given points respet to the line

$y = 2$

In that case, the line beeing paralell to the x- axis, x- value of the symmetry is the same of the given point and y = 2 is the middle between both points.

Point A(1, 1)

$x_{A} = 1\\ x_{A'} = 1 \\\\\frac{y_{A} +y_{A'} }{2} =2\\y_{A'} = 4 - y_{A} = 4 - 1 = 3$