Question:
If the points \( (1, 0), (0, 1) \) and \( (x, 8) \) are collinear, then the value of \( x \) is equal to:
If the points \( (1, 0), (0, 1) \) and \( (x, 8) \) are collinear, then the value of \( x \) is equal to:
Show Hint
The equation of the line passing through \( (1,0) \) and \( (0,1) \) is simply \( x + y = 1 \). By substituting the third point \( (x, 8) \) into this equation: \( x + 8 = 1 \), which immediately gives \( x = -7 \).
Updated On: May 1, 2026
- \( 5 \)
- \( -6 \)
- \( 6 \)
- \( 7 \)
- \( -7 \)
Show Solution
Verified By Collegedunia
The Correct Option is
Solution and Explanation
Concept: Three points are collinear if they lie on the same straight line. This means the slope between any two pairs of points must be equal (\( m_1 = m_2 \)). Alternatively, the area of the triangle formed by these three points must be zero.
Step 1: Equate the slopes.
Points are \( A(1, 0), B(0, 1), C(x, 8) \). \[ \text{Slope of AB } (m_1) = \frac{1-0}{0-1} = -1 \] \[ \text{Slope of BC } (m_2) = \frac{8-1}{x-0} = \frac{7}{x} \] For collinearity, \( m_1 = m_2 \): \[ -1 = \frac{7}{x} \]
Step 2: Solve for \( x \).
\[ -x = 7 \implies x = -7 \]
Was this answer helpful?
0
0
Top KEAM Mathematics Questions
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
- The value of $ \cos [{{\tan }^{-1}}\{\sin ({{\cot }^{-1}}x)\}] $ is
- The solutions set of inequation $\cos^{-1}x < \,\sin^{-1}x$ is
- Let $\Delta= \begin{vmatrix}1&1&1\\ 1&-1-w^{2}&w^{2}\\ 1&w&w^{4}\end{vmatrix}$, where $w \neq 1$ is a complex number such that $w^3 = 1$. Then $\Delta$ equals
- Let $p : 57$ is an odd prime number, $\quad \, q : 4$ is a divisor of $12$ $\quad$ $r : 15$ is the $LCM$ of $3$ and $5$ Be three simple logical statements. Which one of the following is true?
View More Questions
Top KEAM Straight lines Questions
- Area of the triangle with vertices $(- 2, 2), (1, 5) $and $(6, - 1)$ is
- If a straight line passes through the points $ \left( \frac{-1}{2},1 \right) $ and $(1, 2)$, then its $x$-intercept is
- Let $A (6, -1), B (1, 3)$ and $C (x, 8)$ be three points such that $AB = BC$. The values of $x$ are
- The locus of a point which is equidistant from the points $(1,1)$ and $(3, 3)$ is
- Let $O$ be the origin and $A$ be the point $(64, 0).$ If $P$, $Q$ divide $OA$ in the ratio $1 : 2 : 3$ , then the point $P$ is
View More Questions
Top KEAM Questions
- i.$\quad$ They help in respiration ii.$\quad$ They help in cell wall formation iii.$\quad$ They help in DNA replication iv. $\quad$They increase surface area of plasma membrane Which of the following prokaryotic structures has all the above roles?
- A body oscillates with SHM according to the equation (in SI units), $x = 5 cos \left(2\pi t +\frac{\pi}{4}\right) .$ Its instantaneous displacement at $t = 1$ second is
- The pH of a solution obtained by mixing 60 mL of 0.1 M BaOH solution at 40m of 0.15m HCI solution is
Kepler's second law (law of areas) of planetary motion leads to law of conservation of
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
View More Questions