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

Answer:

• (-7, 0) and (7, 0)

Step-by-step 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)

Answer 2

The equation will be

$\\ \sf\longmapsto \sqrt{x^2+y^2}=7$

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

• If y be 0

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

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

$\\ \sf\longmapsto x=\sqrt{49}$

$\\ \sf\longmapsto x=\pm 7$

Now the points are

• (7,0)
• (-7,0)