symmetry and graphs part II

[marshall1432]

1. If a graph is symmetric with respect to the x-axis and the point (3, 2) is on the graph, then what other point is also on the graph?

2. If a graph is symmetric with respect to the x-axis and the point (-4, -2) is on the graph, then what other point is also on the graph?

3. If a graph is symmetric with respect to the x-axis and the point (7, -6) is on the graph, then what other point is also on the graph?

4. If a graph is symmetric with respect to the y-axis and the point (-3, 1) is on the graph, then what other point is also on the graph?

HELP, I CANT GET THE SOLUTIONS!

 

[Mrspi]

1. If a graph is symmetric with respect to the x-axis and the point (3, 2) is on the graph, then what other point is also on the graph?

2. If a graph is symmetric with respect to the x-axis and the point (-4, -2) is on the graph, then what other point is also on the graph?

3. If a graph is symmetric with respect to the x-axis and the point (7, -6) is on the graph, then what other point is also on the graph?

4. If a graph is symmetric with respect to the y-axis and the point (-3, 1) is on the graph, then what other point is also on the graph?

If a graph is symmetric with respect to the x-axis, then the x-axis divides the graph into two identical mirror-image parts. Given ONE point on the graph, you know that there is another point which is on the opposite side of the x-axis, the same distance away from the x-axis. If the point (a, b) is on the graph, then the point (a, -b) is on the graph.

If a graph is symmetric with respect to the y-axis, then the y-axis divides the graph into two identical mirror image parts. For every point of the graph on one side of the y-axis, there is another point on the other side of the y-axis, the same distance away from the y-axis. If the point (a, b) is on the graph, then the point (-a, b) is on the graph.

Drawing a sketch for each situation might be of some help to you.

I'm not going to do your problems for you, but I will give an example of each type.

a) If a graph is symmetric with respect to the x-axis, and the point (-2, 5) is on the graph, give the coordinates of another point which is on the graph. Since we know there is another point of the graph on the opposite side of the x-axis, the same distance away from the x-axis. That point would be (-2, -5).

b) If a graph is symmetric with respect to the y-axis, and the point (-7, -2) is on the graph, give the coordinates of another point which is on the graph. Since we know there is another point of the graphh on the opposite side of the y-axis, the same distance away from the y-axis. That point would be (7, -2).