Absolute Value Area

Algebra Level 3

What is the area of the region of points ( x , y ) (x, y) on the coordinate plane that satisfy the following inequality?

∣ x − 3 ∣ + ∣ y − 6 ∣ ≤ 10 \large |x-3|+|y-6| \le 10


The answer is 200.

Zain Majumder by Zain Majumder , 19, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Tom Engelsman
Feb 2, 2019

The region in question is a square with vertices ( 3 , 16 ) ; ( 3 , − 4 ) ; ( − 7 , 6 ) ; ( 13 , 6 ) (3,16); (3, -4); (-7,6); (13,6) and diagonal length of 20 20 . The required area is the union of two right isosceles triangles:

A = 2 ⋅ 1 2 ( 10 ) ( 20 ) = 200 . A = 2 \cdot \frac{1}{2}(10)(20) = \boxed{200}.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...