Find the value of x for which the points (x, | vedclass

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

Question

(A) If points $A(x, -1), B(2, 1),$ and $C(4, 5)$ are collinear,then the slope of $AB$ must be equal to the slope of $BC$.Slope of $AB = \frac{1 - (-1)

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(A) If points $A(x, -1), B(2, 1),$ and $C(4, 5)$ are collinear,then the slope of $AB$ must be equal to the slope of $BC$.Slope of $AB = \frac{1 - (-1)}{2 - x} = \frac{2}{2 - x}$Slope of $BC = \frac{5 - 1}{4 - 2} = \frac{4}{2} = 2$Equating the slopes: $\frac{2}{2 - x} = 2$$\Rightarrow 2 = 2(2 - x)$$\Rightarrow 2 = 4 - 2x$$\Rightarrow 2x = 2$$\Rightarrow x = 1$Thus,the required value of $x$ is $1$.

Find the value of $x$ for which the points $(x, -1), (2, 1),$ and $(4, 5)$ are collinear.

Similar Questions

Find the equation of a line drawn perpendicular to the line $\frac{x}{4}+\frac{y}{6}=1$ through the point where it meets the $y-$ axis.

Find the equation of the line,which makes intercepts $-3$ and $2$ on the $x$- and $y$-axes respectively.

If the point $(5, 2)$ divides the segment of the line between the axes into two equal parts,then its equation is:

$A$ line passes through $(x_{1}, y_{1})$ and $(h, k)$. If the slope of the line is $m$,show that $k - y_{1} = m(h - x_{1})$.

What is the equation of the line passing through $(-1, 1)$ and perpendicular to the line $2x + 3y + 4 = 0$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module