You will need
  • - handle;
  • paper for records;
  • calculator.
Video on the plane described by the equation: ax+by+C = 0, where x,y – coordinates along axis 0x, and the axis 0у any point of the line; a, b, C – numerical coefficients. Moreover a and b cannot be zero simultaneously. This type of entry is called the General equation of a straight line.
Direct you can specify an expression of the form: y = kx+c. This is the equation of a line with the angular coefficient k, which is the tangent of the angle formed by the intersection of this line with axis 0x.
Knowing the coordinates of two points A (x1, y1), (x2;Y2), you can write the equation of a straight line drawn through these points, using the ratio: (u-U1)/(U1-U2)=(x-x1)/(U1-U2). Then, transforming this equation, bring it to the form as in step 1 or 2.
Consider the algorithm of solving the problem on a concrete example. Given three vertices of a triangle with known coordinates: A (9;8), (7;-6), (-7;4). Write the equation of direct forming it.
As the coordinates of the triangle vertices to find equation of sides
Find the equation for the line AB. Apply the formula from step 3, substituting values of the coordinates of points A and b: (-8)/(8-(-6)) = (x-9)/(9-7). Convert it: (y-8)/14 = (x-9)/2 or 2(y-8) = 14(x-9). Reduce the equation by dividing the left and right sides by two, expand the brackets: y = 7x-63+8 = 7x-55.
The equation for AB is: y = 7x-55. Or: 7x-55 = 0 (AB).
Similarly, write the equation for direct sun: (-(-6))/(-6-4) = (x-7)/7-(-7)). (at+6)/(-10) = (x-7)/14. 7(y+6) = -5(x-7). 7U+42 = -5x+35. 7U = -5x-7. y = -5/7x-1.
The equation for m: y = -5/7x-1. Or: -5x-7U-7 = 0 (Sunday).
Then the equation for a straight SA: (u-8)/(8-4) = (x-9)/(9-(-7)). 16(y-8) = 4(x-9). 4U-32 = x-9. 4U = x-9+32. y = 0.25 x+5,75.
The equation for CA: y = 0.25 x+5,75. Or: x-4U+23 = 0 (SA).
You made the equation three sides of the figure. For the self build triangle in the coordinate system. Locate on the drawing the values of the intersections of straight lines with the axis 0у. Compare these coordinates with those obtained in the equation. For example, for a (BC) when y = 0, x = -1,4.