## Task Condition

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 $a$?

$A(5 ; 0 ;-1)$

$a: 2x - y + 3z - 1 = 0$

$k = 3$
## 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 $a$:

$a^{\prime}: 2 x-y+3 z-3=0$

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

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

$10-3-3=0$

$4=0$

Since $4 \neq 0$, point $A$ does not belong to the image of the plane $a$.

## Problem Kuznetsov Analytical Geometry 12-16