Answer:
Rounding to the nearest tenth, the distance between the point (4, 2) and the line 3x + 2y = 4 is approximately 1.1 units.
Explanation:
To find the distance between a point and a line, we can use the formula for the perpendicular distance from a point to a line. In this case, the given point is (4, 2), and the line is represented by the equation 3x + 2y = 4.The formula for the distance between a point (x1, y1) and a line Ax + By + C = 0 is:Distance = |Ax1 + By1 + C| / √(A^2 + B^2)Let's calculate the distance using this formula:Given line equation: 3x + 2y = 4
Rearranging the equation in the standard form:
2y = 4 - 3x
y = (4 - 3x)/2Comparing with the standard form Ax + By + C = 0:
A = -3, B = 2, C = 4Now substitute the values into the formula:Distance = |(-3)(4) + (2)(2) + 4| / √((-3)^2 + 2^2)
= |-12 + 4 + 4| / √(9 + 4)
= |-4| / √(13)
= 4 / √13