Final answer:
The calculated distance between line K with the equation y = x - 5 and point E(-3,7) is approximately 10.6, so the closest answer option is (c) 10.
Step-by-step explanation:
The question asks for the distance between a line with equation y = x - 5 and a point E(-3,7). To find this distance, we need to use the formula for the distance from a point to a line in a two-dimensional plane which is d = |Ax + By + C| / √(A² + B²), where A, B, and C are the coefficients of the line in the form Ax + By + C = 0, and (x, y) are the coordinates of the point. For the given line y = x - 5, rewriting in the form Ax + By + C = 0 gives us x - y - 5 = 0. Thus, A = 1, B = -1, and C = -5. Plugging the point E(-3, 7) into the equation gives us d = |(1)(-3) + (-1)(7) - 5| / √(1² + (-1)²) = |-3 - 7 - 5| / √2 = |-15| / √2 = 15 / √2, which simplifies to approximately 10.6. Therefore, the closest option provided to this calculated distance is option (c) 10.