The points A(-a, -b),B(0, 0),C(a, b),and D(a^ | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) To check if the points are collinear,we can check the slopes of the line segments formed by these points.Slope of $AB = \frac{0 - (-b)}{0 - (-a)}

Vedclass · Accepted Answer

collinear

Vedclass · Answer

(A) To check if the points are collinear,we can check the slopes of the line segments formed by these points.Slope of $AB = \frac{0 - (-b)}{0 - (-a)} = \frac{b}{a}$.Slope of $BC = \frac{b - 0}{a - 0} = \frac{b}{a}$.Since the slope of $AB$ is equal to the slope of $BC$,the points $A, B,$ and $C$ are collinear.Now,check the slope of $CD = \frac{ab - b}{a^2 - a} = \frac{b(a - 1)}{a(a - 1)} = \frac{b}{a}$ (for $a 
eq 1, a 
eq 0$).Since the slope of $BC$ is equal to the slope of $CD$,the points $B, C,$ and $D$ are also collinear.Since all points lie on the same line with slope $\frac{b}{a}$,the points $A, B, C,$ and $D$ are collinear.

The points $A(-a, -b)$,$B(0, 0)$,$C(a, b)$,and $D(a^2, ab)$ are

Similar Questions

What is the normal form of the line $x + \sqrt{3}y - 4 = 0$?

The number of straight lines which are equally inclined to both the axes is

The gradient of the line joining the points on the curve $y = x^2 + 2x$ whose abscissae are $1$ and $3$,is

What is the equation of the line that makes an angle of $45^{\circ}$ with the $x$-axis and passes through the point $(3, -4)$?

An equation of a line whose segment between the coordinate axes is divided by the point $\left(\frac{1}{2}, \frac{1}{3}\right)$ in the ratio $2: 3$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module