Q. 7 - Precalculus Enhanced with Graphing Utilities

Question

If the graph of an equation is symmetric with respect to the origin and (3, -4) is a point on the graph, then ________ is also a point on the graph.

Step-by-Step Solution

Answer

If the graph of an equation is symmetric with respect to the origin and (3, -4) is a point on the graph, then $\left(-3, 4\right)$ is also a point on the graph.

Step 1: Given information:

The given statement is 

If the graph of an equation is symmetric with respect to the origin and (3, -4) is a point on the graph, then ________ is also a point on the graph.

Step 2:

Symmetric with respect to origin is when the graph remains unchanged if the reflection of both $x-values and y-values$ changes its sign.

Step 3:

On changing the sign of both the given (x, y) point, makes the graph symmetric with respect to origin:

If a graph is symmetric with respect to the origin and the point (3, -4) is on the

graph, then the point (-3, 4) is also on the graph.