Question

Given that the point (1,2) is on the graph of an equation that is symmetric with respect to the origin, what other point is on the graph?

a) (-1, -2)

b) (2, 1)

c) (-2, -1)

d) (1, -2)

Answer 1

The point (1,2) on a graph that is symmetric with respect to the origin implies that the corresponding symmetry point is (-1, -2), which is reflected across both axes.

Step-by-step explanation:

If a point is on the graph of an equation that is symmetric with respect to the origin, then for every point (x, y) on the graph, the point (-x, -y) will also be on the graph. This symmetry means that the graph is unchanged when rotated 180 degrees around the origin or reflected across both the x-axis and y-axis.

Given the point (1,2) is on the graph, by applying this principle of origin symmetry, the corresponding symmetric point on the graph would be (-1, -2). So the other point on the graph would be the one with the x and y values negated from the original point, which is option a) (-1, -2).