Question

If A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4) form two line segments, AB and CD , which condition needs to be met to prove AB is perpendicular to CD?

Answer 1

Condition:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{x_{4}-x_{3}}{y_{4}-y_{3}}$

Explanation:

A(x₁, y₁), B(x₂, y₂), C(x₃, y₃), and D(x₄, y₄)

AB & CD are two lines

Write the condition to prove AB is perpendicular to CD.

Condition of Perpendicularity of Two Lines. We will learn how to find the condition of perpendicularity of two lines. If two lines AB and CD of slopes m and n are perpendicular, then the angle between the lines θ is of 90°. Thus when two lines are perpendicular, the product of their slope is -1.

Here the product of slopes of two lines is -1

Slope of line AB = $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Slope of line CD = $\frac{y_{4}-y_{3}}{x_{4}-x_{3}}$

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{x_{4}-x_{3}}{y_{4}-y_{3}}$

Answer 2

Answer:

Step-by-step explanation:

Given,

Coordinates of A (x1, y2)

Coordinates of B(x2, y2)

Coordinates of C(x3, y3)

According to the question

Coordinates of F=x3+x2/2,y3+y2/2

Coordinates of o= x1+x2+x3/2,y1+y2+y3/2