Solution idea

1. Suppose the coordinates of point A are (x 1, k/x 1) and the coordinates of point B are (x2, k/x2). Since □ABCD is a parallelogram, CD=AB and AD = BC.

2. According to the distance formula between two points, write the length of CD and AD respectively;

3. Because AB∨CD and AD∨BC have equal slopes, their slopes can be found by two-point linear equation;

4. Solve the equation group consisting of Formula ①, Formula ② and Formula ③ to obtain

k = 12，- 12，-24，24

x 1 =-3，3，-3，3

x2=-2，-2，？ 4,? four

According to the known conditions, k>0, x 1, x2>0, finally get k = 24, x 1 =- 3, x2=? four

Solution process

Topic knowledge point

1, parallelogram Two groups of parallelograms whose opposite sides are parallel and equal are called parallelograms. Rectangular, rhombic and square are all special parallelograms. )

Its judgment method:

1, two groups of parallelograms with opposite sides are parallelograms (definition judgment method);

2. A group of quadrilaterals with parallel and equal opposite sides are parallelograms;

3. Two groups of quadrangles with equal opposite sides are parallelograms;

4. Two groups of quadrangles with equal diagonal angles are parallelograms (two groups of opposite sides are judged to be parallel);

5. Quadrilaterals whose diagonals bisect each other are parallelograms.

Supplement: Condition 3 holds only if it is a planar quadrilateral. If it is not a plane quadrilateral, even two sets of quadrilaterals with equal opposite sides are not parallelograms.

2. The distance formula between two points. On the plane, the length of the line segment ending at these two points is the distance between these two points.

3. The condition that two straight lines are parallel.

4. Two-point linear equation. A linear equation expressed by the coordinates of two points on a straight line.