Option fourth: (3j, 3k) and (3/j, 3k) is correct option here.
It is mainly because no matter what j and k be from nonzero integer set, the signs of x and y will be same of both points, thus lying in same quadrant.
Given that:
j and k are non-zero integers.
To find: The pair of points out of given points such that both points lie in the same quadrant.
Explanation:
The whole XY plane is divided into four quadrants. See the image attached below of this post.
The coordinates of a points are written as (x,y) where x (called abscissa) shows position on x axis and y (called ordinate) shows position on y-axis.
The first quadrant (without containing axes) contains (+ve , +ve) which means x must be positive and y must be positive.
The second quadrant has (-ve, +ve)
The third quadrant has (-ve, -ve)
and the fourth quadrant has ( -ve, +ve)
The axes contains (0,+ve), (+ve,0), (0,-ve), (-ve, 0) and their intersection O contains (0, 0)
Checking of options:
Option A: (j, j) and (k, k)
A contrary example is when j = 2 and k = -2, then (j,j) will belong to first quadrant and (k,k) will belong to third quadrant.
Option B: (j,k) and (jk, jk)
A contrary example is when j = -2 and k = -2, then jk = +4, thus, we have:
(j,k) = (-2,-2) (belonging to third quadrant)
and (jk,jk) = (4,4) (belonging to first quadrant)
Option C: (j + k, 3) and (3, j + k)
A contrary example is when j = 1 and k = -2, then j + k = -1
and thus:
(j+k,3) = (-1,3) (belonging to second quadrant)
and (3, j+k) = (3, -1) belonging to fourth quadrant.
Option D: (3j, 3k) and (3/j, 3k)
This option is the correct option. It is because:
Sign of 3j = sign of 3/j for both positive and negative j
Sign of 3k = sign of 3/k for both positive and negative k
Thus (3j,3k) will have same sign pair as of (3/j, 3/k). Thus they will belong to same quadrant.
Learn more about quadrants here:
https://brainly.com/question/350459
