GATE Civil 2022 Set 1 | GA Question: 2

Question

Two straight lines pass through the origin $(x_{0}, y_{0}) = (0, 0)$. One of them passes through the point $(x_{1}, y_{1}) = (1, 3)$ and the other passes through the point $(x_{2}, y_{2}) = (1, 2)$.

What is the area enclosed between the straight lines in the interval $[0, 1]$ on the $x$-axis?

• A. $0.5$
• B. $1.0$
• C. $1.5$
• D. $2.0$

Answer 1

Let’s first draw the diagram.

The area enclosed between the straight lines in the interval $[0,1]$ on the $x$-axis $ = \text{area of}\;\triangle \text{ACO} – \text{area of}\;\triangle \text{BCO}$

$= \dfrac{1}{2} \times 1 \times 3\; – \dfrac{1}{2} \times 1 \times 2 = \dfrac{1}{2}(3-2) = \dfrac{1}{2} = 0.5\;\text{unit}^{2}.$

Correct Answer $:\text{A}$

$\textbf{PS:}$ The area of triangle ${\color{Green}{ = \dfrac{1}{2} \times \text{Base} \times \text{Height}}}$