The Perpendicular Distance from a Point to a Line: d=|(A x1+B y1+C)/(√(A^2+B^2))| The perpendicu

step 1 Here in this question the perpendicular distance from a point to a line is given by D equals to

The Perpendicular Distance from a Point to a Line: d=|(A...

The Perpendicular Distance from a Point to a Line: $d=\left|\frac{A x_{1}+B y_{1}+C}{\sqrt{A^{2}+B^{2}}}\right|$ The perpendicular distance from a point $\left(x_{1}, y_{1}\right)$ to a given line can be found using the formula shown, where $A x+B y+C=0$ is the equation of the line in standard form $(A, B, \text { and } C$ are integers). Use the formula to verify that $P(-6,2)$ and $Q(6,4)$ are an equal distance from the line $y=-\frac{1}{2} x+3$ .

The Perpendicular Distance from a Point to a Line: $d=\left|\frac{A x_{1}+B y_{1}+C}{\sqrt{A^{2}+B^{2}}}\right|$ The perpendicular distance from a point $\left(x_{1}, y_{1}\right)$ to a given line can be found using the formula shown, where $A x+B y+C=0$ is the equation of the line in standard form $(A, B, \text { and } C$ are integers).
Use the formula to verify that $P(-6,2)$ and $Q(6,4)$ are an equal distance from the line $y=-\frac{1}{2} x+3$ .

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Standard Form of a Line

A line can be expressed in the standard form Ax + By + C = 0, which is useful for many calculations in coordinate geometry. This form makes it straightforward to identify the coefficients that are used in formulas like the perpendicular distance formula.

Conversion of Line Equations

Lines are often given in slope-intercept form, but converting them to standard form is essential when applying the perpendicular distance formula. This conversion involves rearranging the equation to align with the Ax + By + C = 0 structure.

Perpendicular Distance Formula

This formula calculates the shortest distance from a point to a line by projecting the point onto a normal (perpendicular) direction relative to the line. It uses the coefficients of the line’s standard form and incorporates the absolute value to ensure the distance is non-negative.

Verification of Equal Distances

Verifying that two points are equidistant from a line involves calculating their individual perpendicular distances using the same formula. This comparison relies on accurate computation and understanding of the distance formula within the coordinate system.

Transcript

Please give Ace some feedback