Question

Find all of the points of the form (x, −x) which are 7 units from the origin.

(x, y) =

(smaller x-value)

(x, y) =

(larger x-value)

Answer 1

The equation will be

`\\ \sf\longmapsto √(x^2+y^2)=7`

`\\ \sf\longmapsto x^2+y^2=7`

• If y be 0

`\\ \sf\longmapsto x^2+0=7^2`

`\\ \sf\longmapsto x^2=49`

`\\ \sf\longmapsto x=√(49)`

`\\ \sf\longmapsto x=\pm 7`

Now the points are

• (7,0)
• (-7,0)

Answer 2

• (-7, 0) and (7, 0)

Explanation:

All the points that are 7 units from the origin are on the circle:

• x² + y² = 7²

The maximum and minimum values of x obtained when y = 0:

• x² = 7²
• √x² = √7²
• x = ± 7

So

• min x = -7 and
• max x = 7

The points are:

• (-7, 0) and (7, 0)