The distance of point P (6, -1) from the line 6x – 4y + 9 = 0 is:A.4949B.49524952C.√49524952D.49√52

To find the distance of point P (6, -1) from the line 6x - 4y + 9 = 0, we can use the formula for the distance between a point and a line.

1. First, we need to rewrite the equation of the line in slope-intercept form (y = mx + b). Rearranging the given equation, we have: 6x - 4y + 9 = 0 -4y = -6x - 9 y = (3/2)x + (9/4)

2. Now that we have the equation of the line in slope-intercept form, we can find the slope (m) of the line. In this case, the slope is 3/2.

3. Next, we can use the formula for the distance between a point (x1, y1) and a line (Ax + By + C = 0): Distance = |Ax1 + By1 + C| / √(A^2 + B^2)

   Plugging in the values, we have: Distance = |(6)(6) + (-4)(-1) + 9| / √((6)^2 + (-4)^2) = |36 + 4 + 9| / √(36 + 16) = |49| / √52 = 49 / √52

4. Simplifying the expression, we can rationalize the denominator by multiplying both the numerator and denominator by √52: Distance = (49 / √52) * (√52 / √52) = (49√52) / 52

Therefore, the distance of point P (6, -1) from the line 6x - 4y + 9 = 0 is D. 49√52.