CAT 2024 Slot 2 QA Q14 Coordinate Geometry

Question 14 of the Quantitative Ability (QA) section, CAT 2024 Slot 2, with CAT's official answer and a worked solution.

The coordinates of the three vertices of a triangle are: (1, 2), (7, 2), and (1, 10). Then the radius of the incircle of the triangle is

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

Answer: 2 Coordinate Geometry TITA

Solution

  1. The vertices give a right angle at \((1,2)\): legs \(7-1 = 6\) and \(10-2 = 8\).
  2. Hypotenuse \(= \sqrt{36+64} = 10\).
  3. Inradius of a right triangle \(= \frac{6+8-10}{2} = 2\).

Shortcut. \(r = \frac{a+b-c}{2}\) for a right triangle.

Same concept in other years

See every question on Incircle of a right triangle: r = (a + b − c)/2.

More Coordinate Geometry questions from CAT

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