Final answer:
To determine the distance between point P (-1, 5) and line L containing points (0, -2) and (6, 6), we use the point-line distance formula after finding the standard form equation of line L. The resulting distance is found to be 5 meters.
Step-by-step explanation:
To find the distance from a point to a line in Cartesian coordinates, we can use the point-line distance formula. First, we determine the equation of line L using points (0, -2) and (6, 6). The slope of L is (6 - (-2)) / (6 - 0) = 8 / 6 = 4 / 3. Now, using point-slope form we get the equation of the line L: y + 2 = (4/3)(x - 0), or y = (4/3)x - 2. The point-line distance formula is |Ax1 + By1 + C| / sqrt(A^2 + B^2), where A, B, and C are the coefficients from the line's equation in standard form Ax + By + C = 0 and (x1, y1) are the coordinates of point P. Converting our line equation to standard form gives us 4x - 3y - 6 = 0. Thus, A = 4, B = -3, and C = -6. The coordinates of P are (-1, 5). Finally, we calculate the distance: |4*(-1) - 3*5 - 6| / sqrt(4^2 + (-3)^2) = | -4 - 15 - 6| / sqrt(16 + 9) = | -25 | / sqrt(25) = 25 / 5 = 5 meters.