Final answer:
To find the distance between line y = -x + 2 and the point R(0, -4), use the perpendicular distance formula. The calculated distance is approximately 4.24 units.
Step-by-step explanation:
The question asks us to find the distance between a given line l with the equation y = -x + 2 and a specific point R(0, -4). The most efficient way to find this distance is to use the perpendicular distance formula, which gives the shortest distance between a point and a line. This formula is derived using the coefficients of the line's equation and the coordinates of the point.
To apply the formula, we'll need the equation of the line in the form Ax + By + C = 0. For the equation y = -x + 2, it can be rewritten as x + y - 2 = 0, where A = 1, B = 1, and C = -2. Using the point R(0, -4), where x0 = 0 and y0 = -4, the perpendicular distance d is calculated by:
d = |A * x0 + B * y0 + C| / √(A² + B²)
Substituting the values we have:
d = |1 * 0 + 1 * (-4) - 2| / √(1² + 1²) = |-6| / √2 = 6 / √2 = 3√2 (approx. 4.24 units).
The distance between line l and point R is approximately 4.24 units.