Question

7. Three vertices of a parallelogram are (0, 0), (−4,0) and (0, 5). Find all 3 possible coordinates for

Answer 1

The given vertices combine with the fourth vertex as follows;

a) Coordinates; (-4, 5)

Lengths of the sides; 4 and 5

b) Coordinates; (4, 5)

Lengths of the sides; 4 and √41

c) Coordinates; (-4, -5)

Lengths of the sides; 5 and √41

How can the vertex coordinates be found?

The given vertices are;

(0, 0): The origin

(-4, 0): 4 units to the left of the origin along the abscissa

(0, 5): 5 units above the origin, along the ordinate

a) The point that forms a rectangle is above the point (-4, 0) and to the left of the point (0, 5), which gives;

The coordinates of the point that forms a rectangle is the point (-4, 5)

The lengths of the sides are;

0 - (-4) = 4

5 - 0 = 5

b) The first parallelogram is formed by moving an equal distance of the point (-4, 0) from the origin from the point (0, 5), which gives;

• The first parallelogram is formed by the point (4, 5)

The lengths of the sides are;

• 4 - 0 = 4
• √((5 - 0)^2 + (4 - 0)^2) = √41

c) The second parallelogram is formed by the moving an equal distance of the point (0, 5) from the origin from the point (-4, 0), which gives;

• The second parallelogram is formed by the point (-4, -5)

The lengths of the sides are;

• (5 - (-5)) = 5 and √41

Learn more about parallelograms here:

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