A plane is a flat, two-dimensional [2d] plane that stretches indefinitely. It is a two-dimensional representation of a point, a line, and a three-dimensional space. The equation denotes a plane in three dimensions.

ax + by + cz + d=0,

a, b and c are non-zero.

A Brief Outline

In three-dimensional coordinate space, a point, as well as a vector, are perpendicular to the surface, which establishes the plane.

Important Concepts

How to Find a Picture of a Point in a plane

1. Take a look at the two points P and Q. Let be a plane in which a perpendicular line PQ to the plane exists.
2. The plane is where PQ’s midpoint is. The point’s image is either of the points in the plane that are next to one another. To find the image of a point in a given plane, follow these steps:
3. The normal to the particular plane and the line passing across point P have the following equations:

x-x1/a, y-y1/b, z-z1/c

• (x1+ ar, y1 + br, z1 + cr) are the coordinates of the picture Q.
• The coordinates of PQ’s mid-point R are discovered.
• Substituting R’s coordinates into the planar equation yields the value of r.
• Lastly, the r-value is entered into Q’s coordinates.

Because the object and the image are in opposing directions when we estimate distances from the mirror, the object and image distances for a flat mirror should have opposite signs. An extended object, such as the container, can be thought of as a collection of points, and we can apply the method described above to find the image of each point on the stretched object, resulting in the extended image.

Significance of how to find an image of a point in a plane in the IIT JEE exam

A solid understanding of mathematics is required to understand the image of a point in a plane. Only queries based on equations will be answered. Roughly 2 questions are being asked on the IIT JEE exam, making for 6.66 percent of the total.

FAQs

What does a point's image look like?

In a mirror, the reflection of a point P is designated P’ and is referred to as point P’s “image.” If you look closely at the diagram above, you’ll notice that the point P’, which is P’s image, is at the same range from the mirror as P.

In Coordinate Geometry, what is a Mirror Image?

On the x-axis, the mirror image of point P (x, y) becomes P. (x, -y). To locate the image of the point along the x-axis, we keep the x-coordinate the same and change the sign of the y-coordinate. On the mirror, every single point remains the same.

How can you tell if a line is parallel to a plane?

As a result, there is a plane test to see any two points from the line. If this is the case, all of the line's points should be on the surface, and the line, therefore, lies on the surface. If not, it's either the first or second scenario.