Question

the point such as (0,x) (0,-x) (0,y) (0,-y)lie on the same line name the line

Answer 1

answer : y - axis

explanation : in two dimensional co-ordinate geometry, horizontal line is assumed as x - axis (absissa) and vertical line is assumed as y - axis( ordinate). and point is written as (x, y).

in x-axis , value of y become zero e.g., general form of points in x-axis is (±a, 0), where a is real numbers.

and in y-axis , value of x becomes zero. e.g., general form of points in y-axis is (0, ±b) , where b is real numbers.

here given, points are ; (0, x), (0, -x), (0, y), (0, -y).

did you noticed that,

value of x = 0 for all given points

so, these points lie on Y-axis.

so, name of line is y-axis.

Answer 2

Answer:

x=∞ and y=∞ contains all the given points .

if mathematical proof is required , we can infer the result by finding slope :

m=  (y2-y1)/(x2-x1)

m=    -x-x/(0-0)= ∞

since m=∞ , we can get y=∞ .

similarly , take (0,y) and (0,-y) to get x=∞

Step-by-step explanation :