Final answer:
The distance from the point (5,8) to the line 3x+3y=-9 is found using a specific distance formula which results in d = 5 * sqrt(2), or approximately 7.071 units.
Step-by-step explanation:
The subject of this question is mathematics, specifically, geometry. The question asks you to find the distance from a point, specifically the point (5,8), to a line. The equation given for the line is 3x + 3y = -9. First, let's normalize the equation for the line by dividing it by 3, so we have x + y = -3. The distance (d) from a point to a line can be calculated using the formula d = |Ax1 + By1 + C| / sqrt(A^2 + B^2), where (x1, y1) is the point, and Ax + By + C = 0 is the line equation. Substituting the line equation's coefficients (A=1, B=1 and C=-3) and the coordinates of the point x1 = 5 and y1 = 8 into the formula, we get d = |(1*5) + (1*8) - 3| / sqrt(1^2 + 1^2) = |10| / sqrt(2) = 10/sqrt(2). Rationalizing the denominator we get d = 5 * sqrt(2), approximately equal to 7.071. So, the distance from point (5,8) to the line 3x+3y=-9 is approximately 7.071 units.
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