CAT 2023 Slot 2 QA Q19 Coordinate Geometry

Question 19 of the Quantitative Ability (QA) section, CAT 2023 Slot 2, with CAT's official answer and a worked solution.

The area of the quadrilateral bounded by the \(Y\)-axis, the line \(x=5\), and the lines \(|x-y|-|x-5|=2\), is

TITA: type in the answer. There are no options and no negative marking.

Answer: 45 Coordinate Geometry TITA

Solution

The region lies between \(x = 0\) and \(x = 5\), where \(|x-5| = 5 - x\). So \(|x - y| = 7 - x\).
Then \(y - x = \pm(7-x)\), giving the lines \(y = 7\) and \(y = 2x - 7\).
Vertices: \((0,7), (5,7), (5,3), (0,-7)\). It is a trapezium with vertical parallel sides 14 (at \(x=0\)) and 4 (at \(x=5\)) and width 5.
Area \(= \frac{14 + 4}{2} \times 5 = 45\).