## Problem Statement

Let $k$ be the coefficient of similarity transformation with the center at the origin. Is it true that point $A$ belongs to the image of plane $a$?

$A(1 ; 2 ; 2)$

$a: 3x - z + 5 = 0$

$k = -\frac{1}{5}$
## Solution

When transforming similarity with the center at the origin of the coordinate plane

$a: A x+B y+C z+D=0$ and the coefficient $k$ transitions to the plane

$a^{\prime}: A x+B y+C z+k \cdot D=0$. We find the image of the plane $a$:

$a^{\prime}: 3 x-z-1=0$

Substitute the coordinates of point $A$ into the equation $a^{\prime}$:

$3 \cdot 1-2-1=0$

$3-2-1=0$

$0=0$

Since $0=0$, point $A$ belongs to the image of the plane $a$.

Problem Kuznetsov Analytical Geometry 12-28