Question

write a point whose x coordinate and Y co-ordinate are equal in magnitude but opposite to sign​

Answer 1

Coordinate Geometry

To find: We have to find such points whose $x-$ coordinate and $y-$ coordinate are equal in magnitude but opposite in sign.

Solution:

Let any point in Cartesian plane, has coordinates $(x,\:y)$.

Then the point whose $x-$ coordinate and $y-$ coordinate be equal in magnitude but opposite in sign, is $(-x,\:-y)$, since $|-x|=x$ and $|-y|=y$.

Example points:

1. When $x=1,\:y=1$, such points are $(1,\:1)$ and $(-1,\:-1)$.
2. When $x=1,\:y=2$, such points are $(1,\:2)$ and $(-1,\:-2)$.
3. When $x=2,\:y=1$, such points are $(2,\:1)$ and $(-2,\:-1)$.
4. When $x=2,\:y=2$, such points are $(2,\:2)$ and $(-2,\:-2)$.
5. When $x=-1,\:y=1$, such points are $(-1,\:1)$ and $(1,\:-1)$.