Question

Find the distance of the point (1, -1) from the line 4x + 3y = 9.

a) 2 units
b) 3 units
c) 4 units
d) 5 units

Answer 1

The distance of the point (1, -1) from the line 4x + 3y = 9 is calculated using the distance from a point to a line formula. The correct distance is found to be 1.6 units, which is not listed in the given options.

Step-by-step explanation:

To find the distance of the point (1, -1) from the line 4x + 3y = 9, we use the formula for distance from a point to a line in a two-dimensional Cartesian coordinate system:

The distance d from a point (x0, y0) to a line Ax + By + C = 0 is given by:

d = |Ax0 + By0 + C| / √(A² + B²)

First, rewrite the line equation in the standard form:

4x + 3y - 9 = 0

Then plug the point (1, -1) into the formula:

d = |(4×1) + (3×-1) - 9| / √(4² + 3²)

d = |4 - 3 - 9| / √(16 + 9)

d = | -8 | / √25

d = 8 / 5

d = 1.6

Therefore, the correct answer is not listed in the options provided. The actual distance is 1.6 units.