Question

the coordinates of three of the vertices of a parallelogram are given. Find the possible coordinates for the fourth vertex. L (0,4), M (6,0), N (2,4).

Answer 1

The three possible vertices are: (8,0),(-4,8) and (4,0)

Explanation:

(P is used as our variable point)

If we are solving for a point that would be parallel to L we can use:

M+N-L

For the X value the equation would be (6+2-0)

For the Y value the equation would be (0+4-4)

This gives us a coordinate point of (8,0)

We can verify this point by use the distance formula and comparing segments

In this case LM = NP andMP = LN

If we are solving for a point that would be parallel to M we can use:

L+N-M

For the X value the equation would be (0+2-6)

For the Y value the equation would be (4+4-0)

This gives us a coordinate point of (-4,8)

We can verify this point by use the distance formula and comparing segments

In this case PN = LM and PL = NM

Finally if we are solving for a point that would be parallel to N

L+M-N

For the X value the equation would be (0+6-2)

For the Y value the equation would be (4+0-4)

This gives us a coordinate point of (4,0)

We can verify this point by use the distance formula and comparing segments

In this case LN = PM and LP = NM

Answer 2

Explanation:

Given Coordinates of three vertices of the parallelogram L(0,4), M(6,0), N(2,4).

Corresponding to each vertex, there are three possibilities of having a fourth vertex

Coordinates of fourth vertex opposite to L is given by

(x,y)

(6+2−0,0+4−4)=(8,0)

Coordinates of fourth vertex opposite to M is given by

(x,y)=(0+2−6,4+4−0)=(−4,8)

Coordinates of fourth vertex opposite to N is given by

(x,y)=(0+6−2,4+0−4)=(4,0)

Therefore, the possible coordinates of the fourth vertex are

(8,0);(−4,8) and(4,0)