Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What is the formula to calculate the distance from a line to a point not on the line?

1. d = |Ax₁ + By₁ + C| / √(A² + B²)

2. d = |Ax + By + C| / √(A² + B²)

3. d = |Ax₁ + By + C| / √(A + B)

4. d = |Ax + By₁ + C| / √(A + B²)

The correct answer is: d = |Ax₁ + By₁ + C| / √(A² + B²)

The correct formula to calculate the distance from a line given by the equation \(Ax + By + C = 0\) to a point \((x_1, y_1)\) not on the line is indeed expressed as \(d = \frac{|Ax_1 + By_1 + C|}{\sqrt{A^2 + B^2}}\). This formula allows you to find the shortest distance (perpendicular distance) from the given point to the line. In this expression, \(A\), \(B\), and \(C\) are the coefficients from the line equation, representing the linear relationship in the Cartesian coordinate system. The absolute value ensures that the distance is a non-negative quantity, as distance cannot be negative regardless of the point's position relative to the line. The denominator \(\sqrt{A^2 + B^2}\) normalizes the distance by the length of the vector normal to the line, ensuring that the distance is accurate compared to the slope of the line. The other choices do not properly represent the required formula. They either include incorrect variables (like using \(y\) instead of \(y_1\) when calculating the distance from a point) or misinterpret