## 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 $a$?

$A(5 ; 0 ;-6)$

$a: 6x - y - z + 7 = 0$

$k = \frac{2}{7}$
## Solution

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

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

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

$a^{\prime}: 6 x-y-z+2=0$

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

$6 \cdot 5-0-(-6)+2=0$

$30-0+6+2=0$

$38=0$

Since $38 \neq 0$, point $A$ does not belong to the image of the plane $a$.

## Problem Kuznetsov Analytical Geometry 12-27