Question

What is the distance between the point (2, -3) and the line going through the points (1, -5/4) and (1/3, -3/4)?

a. 2.5
b. 3.0
c. 3.5
d. 4.0

Answer 1

To find the distance between a point and a line in a coordinate plane, we can use the formula for the distance between a point and a line. For the given points, the distance is approximately 3.5 units.

Step-by-step explanation:

To find the distance between a point and a line, we can use the formula for the distance between a point and a line in a coordinate plane.

1. Find the equation of the line passing through the given points.
2. Use the formula d = |Ax + By + C| / sqrt(A^2 + B^2) to calculate the distance.

Substituting the given values into the equation, we get d = |(2)(1) + (-3)(1) + (-5/4)(2) / sqrt((1)^2 + (-5/4)^2).

Simplifying, we have d = |2 - 3 - 5/2| / sqrt(1 + 25/16).

Therefore, the distance between the point (2, -3) and the line passing through the points (1, -5/4) and (1/3, -3/4) is approximately 3.5 units.