Write the equations of four lines that intersect to form a square whose sides are not parallel to the axes.
Where would I start, and how would I complete this?
Thank you so much in advance!
line through (0,0) and (1,1)
line through (1,1) and (0,2)
line through (0,2) and (-1,1)
line through (-1,1) and (0,0)
is one (admittedly unimaginative) way.
Now do a cube :)
PARALLEL (slope is same & intercept is different)
LINE 1: x-1
LINE 2: x+1
PERPINDICULAR (slope has flipped fraction & opposite sign)
LINE 3: -x-1
LINE 4: -x+1
To find the equations of four lines that intersect to form a square with sides not parallel to the axes, we can use the following steps:
1. Start by visualizing the square and understanding its properties. Since the sides are not parallel to the axes, each side will have a slope different from zero.
2. Let's assume that the square intersects the coordinate axes at points A, B, C, and D, in a counterclockwise direction.
3. Determine the coordinates of the four points A, B, C, and D. Choose any arbitrary coordinates for one point, and then use the properties of a square to determine the coordinates of the other three points. Since the length of each side of a square is equal, you can use the distance formula or Pythagorean theorem to calculate the length of the sides and find the coordinates.
4. Find the slopes of the four sides of the square. Use the coordinates of each pair of adjacent points to find the slope of the line passing through them. Remember that the slopes of opposite sides of a square are negative reciprocals of each other.
5. Use the point-slope form of a linear equation to determine the equations of the four lines. The point-slope form of a line is given by y - y1 = m(x - x1), where (x1, y1) are the coordinates of a point on the line, and m is the slope of the line.
6. Substitute the coordinates of the points A, B, C, and D, along with their corresponding slopes, into the point-slope form equation to obtain the four linear equations.
By following these steps, you should be able to determine the equations of four lines that intersect to form a square whose sides are not parallel to the axes.