Question
(2,0):x*2+y*2-4=0
use symmetry to find at least one more point on the graph
use symmetry to find at least one more point on the graph
Answers
GPT 3.5
To find another point on the graph using symmetry, we can use the point that is the reflection of the given point (2,0) across the line x = 2.
The reflection of the point (2,0) across the line x = 2 will have the same y-coordinate and the x-coordinate will be 4 units away from the line x = 2. So, the x-coordinate of the reflected point will be 2 - 4 = -2.
Therefore, the reflected point is (-2,0). This point also satisfies the equation x*2 + y*2 - 4 = 0, so (-2,0) is another point on the graph of the equation.
Thus, the points (2,0) and (-2,0) are symmetrically related and lie on the graph of the equation x*2 + y*2 - 4 = 0.
The reflection of the point (2,0) across the line x = 2 will have the same y-coordinate and the x-coordinate will be 4 units away from the line x = 2. So, the x-coordinate of the reflected point will be 2 - 4 = -2.
Therefore, the reflected point is (-2,0). This point also satisfies the equation x*2 + y*2 - 4 = 0, so (-2,0) is another point on the graph of the equation.
Thus, the points (2,0) and (-2,0) are symmetrically related and lie on the graph of the equation x*2 + y*2 - 4 = 0.