Mathematics

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

#### Nina34

4 years ago

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!