Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
79 views
in Aptitude by (114k points)
closed by

Set A contains points whose abscissa and ordinate are both natural numbers. Point B, an element in set A has the property that the sum of the distances from point B to point (3,0) and the point (0,5) is the lowest among all elements in set A. What is the sum of abscissa and ordinate of point B?


1. 2
2. 4
3. 6
4. Cannot be determined

1 Answer

0 votes
by (115k points)
selected by
 
Best answer
Correct Answer - Option 2 : 4

Calculation:

Any point on the line (x/3) + (y/5) = 1 will have the shortest overall distance.

However, we need to have integral coordinates. So, we need to find the points with integral coordinates as close as possible to the line 5x + 3y = 15.

∴ Substitute x =1, we get y = 2 or 3

∴ Substitute x = 2, we get y = 1 or 2

∴ Sum of distances for (1, 2) = √8 + √10

∴ Sum of distances for (1, 3) = √13 + √5

∴ Sum of distances for (2, 1) = √2 + √20

∴ Sum of distances for (2, 2) = √5 + √13

⇒ √5 + √13 is the shortest distance.

∴ Sum of abscissa + ordinate is 4.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...