Assertion (A): The area enclosed by | x | + | y | = 3 is 18 square units. Reason (R): The region | x | + | y | ≤ 3 is symmetric about both axes, and its part in the first quadrant is the triangle bounded by x + y = 3 and the axes.

Question 18

MediumOriginal question

Assertion (A): The area enclosed by $\lvert x \rvert + \lvert y \rvert = 3$ is 18 square units.
Reason (R): The region $\lvert x \rvert + \lvert y \rvert \le 3$ is symmetric about both axes, and its part in the first quadrant is the triangle bounded by $x + y = 3$ and the axes.

Both A and R are true, and R is the correct explanation of A.Correct answerYour answerBoth A and R are true, but R is not the correct explanation of A.Correct answerYour answerA is true, but R is false.Correct answerYour answerA is false, but R is true.Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

In the first quadrant $\lvert x \rvert + \lvert y \rvert = 3$ is $x + y = 3$ , and $\int_0^{3} (3 - x)\,dx = \frac{9}{2}$ . R is true.
By that symmetry the area is $4 \times \frac{9}{2} = 18$ : A is true, and R is the reason.

Worth noting

The first-quadrant triangle alone is $\frac{9}{2}$ ; the symmetry in R is what multiplies it by 4.

Concept: Using symmetry
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsRegions with lines

Practise this chapter →

Ten questions from Area of Bounded Regions, at your own pace.

Explanation