Question

Find the image of (-2, 3, 4) in the YZ plane.

Answer 1

Hint: The image of a point with respect to a plane is a point which is in the opposite direction to the plane at an equal distance, and the line joining the point and its image is perpendicular to the plane.

Complete step-by-step answer:
Let the point be A(-2, 3, 4).

Let the point B be the image of the point A with respect to the YZ plane as shown in the figure. AB is the line joining the two points and is perpendicular to the YZ plane.

In the figure we can see the distance of point A from the three planes, as represented by the dotted lines. These distances are-
XY plane - 4 units
YZ plane - 2 units
XZ plane - 3 units

We can see that the line AB is parallel to the x- axis, which is represented by the red line. Clearly, as we move along the line AB, only the x-coordinates of the points will change. We know that point B will be at an equal distance from the YZ plane as A, so its distance will also be 2 units, but in the opposite directions.

So for point B,
XY plane - 4 units
YZ plane - 2 units(opposite side)
XZ plane - 3 units

Hence the coordinates are B(2, 3, 4).

This is the required answer.

Note: In such questions regarding the image of a point with respect to the coordinate planes or lines, we can use simple geometry to find the coordinates of the image. We can just draw a rough diagram to see which coordinate is changing, and the respective coordinate becomes the negative of the coordinate of the original point.