Question

The point that is symmetric with respect to the y-axis to the point $(-2,5)$is $\_\_\_\_\_$.

Short answer

The point that is symmetric with respect to the y-axis to the point $(-2,5)is\mathbf{(}\mathbf{2}\mathbf{,}\mathbf{5}\mathbf{)}$.

Step-by-step solution

Step 1. Given Information

Given Point:

$(-2,5)$

We want to find the point that is symmetric to the given point with respect to the y-axis.

Step 2. Understanding symmetry:

When a point $P(x,y)$is given, to find the symmetrical point with respect to the x-axis we must change the sign of the y-coordinates of that point.

Similarly, to find the symmetrical point with respect to the y-axis we must change the sign of the x-coordinates.

The following drawing show why the previous statement hold:

For example, say that the given point is A(3,4), then by changing the sign of the first coordinates, 3, result is a point B(-3,4) that has the same distance from both coordinates axes but it has changed the side with respect to y-axis.

That is symmetric of the point A with respect to y-axis.

A similar statement holds for the symmetry with respect to x-axis.

Step 3. Finding the wanted symmetric point:

Using the previous logic, if we want a point that is symmetric with respect to the y-axis, change the x-coordinate.

The result is therefore$(2,5)$