Final answer:
To find the distance between a point and a line, we need to find the perpendicular distance by using the formula for the perpendicular distance between a point and a line. In this case, the distance between the point (1, 1/2) and the line with slope -3/4 passing through (5/3, -5/4) is 35/12√13.
Step-by-step explanation:
To find the distance between a point and a line, we need to find the perpendicular distance. First, let's find the equation of the line using the slope-intercept form y = mx + b, where m is the slope. We are given the point (5/3, -5/4) and the slope -3/4, so the equation of the line is y = (-3/4)x + (37/12).
Now, let's find the perpendicular distance between the point (1, 1/2) and the line. The formula for the perpendicular distance between a point (x1, y1) and a line ax + by + c = 0 is d = |ax1 + by1 + c| / sqrt(a^2 + b^2). Plugging in the values, we get d = |(-3/4)(1) + 1/2(-3/4) + (37/12)| / sqrt((-3/4)^2 + (1/2)^2).
Simplifying the equation, we find d = 35/12√13.