Question:
Let $A(-1,\,2)$, $B(1,\,-2)$ and $C(-2,\,-2)$ be vertices of the triangle $ABC$. The equation of the line passing through $C$ and parallel to $AB$ is
Let $A(-1,\,2)$, $B(1,\,-2)$ and $C(-2,\,-2)$ be vertices of the triangle $ABC$. The equation of the line passing through $C$ and parallel to $AB$ is
Show Hint
Parallel lines have equal slopes. Once you find the slope of the reference line, directly apply point-slope form with the given point to get the parallel line's equation.
Updated On: Apr 25, 2026
- $x + 2y + 6 = 0$
- $2x - y + 6 = 0$
- $2x + y - 6 = 0$
- $2x - y - 6 = 0$
- $2x + y + 6 = 0$
Show Solution
Verified By Collegedunia
The Correct Option is
Solution and Explanation
Step 1: Understanding the Concept:
A line parallel to $AB$ has the same slope as $AB$. Use point-slope form with point $C$.
Step 2: Detailed Explanation:
Slope of $AB = \dfrac{-2-2}{1-(-1)} = \dfrac{-4}{2} = -2$.
Line through $C(-2,\,-2)$ with slope $-2$:
\[ y - (-2) = -2(x - (-2)) \implies y + 2 = -2x - 4 \implies 2x + y + 6 = 0 \]
Step 3: Final Answer:
The required equation is $2x + y + 6 = 0$.
A line parallel to $AB$ has the same slope as $AB$. Use point-slope form with point $C$.
Step 2: Detailed Explanation:
Slope of $AB = \dfrac{-2-2}{1-(-1)} = \dfrac{-4}{2} = -2$.
Line through $C(-2,\,-2)$ with slope $-2$:
\[ y - (-2) = -2(x - (-2)) \implies y + 2 = -2x - 4 \implies 2x + y + 6 = 0 \]
Step 3: Final Answer:
The required equation is $2x + y + 6 = 0$.
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