## 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 $a$?

$A(2; -3; 1)$

$a: x + y - 2z + 2 = 0$

$k = \frac{5}{2}$
## 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 $a$:

$a^{\prime}: x+y-2 z+5=0$

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

$2-3-2 \cdot 1+5=0$

$2-3-2+5=0$

$2=0$

Since $2 \neq 0$, point $A$ does not belong to the image of the plane $a$.

Problem Kuznetsov Analytical Geometry 12-10