Question

multiple-choice question a change in the x value means the preimage slides... up or down right or left which line of reflection is the vertical line that passes through the origin? a horizontal line that goes through y=k (k is not zero). a vertical line that goes through x=k (k≠0) the y-axis the x-axis rewatch

Explanation:

First Question (About Translation):

Step1: Recall translation concepts

In a coordinate system, when the \( x \)-value of a point (preimage) changes, it causes a horizontal (left or right) shift. Vertical shifts are caused by changes in the \( y \)-value.

Step2: Match with options

The option "right or left" corresponds to horizontal translation, which is caused by a change in the \( x \)-value. The "up or down" is vertical translation (change in \( y \)-value), and "A change in the \( x \) value..." is the description, not the direction. So the correct direction for \( x \)-value change is horizontal (right/left).

Step1: Recall vertical lines

A vertical line has an undefined slope and is of the form \( x = k \), where \( k \) is a constant. The origin has coordinates \( (0,0) \), so a vertical line through the origin must satisfy \( x = 0 \), which is the \( y \)-axis? Wait, no: Wait, the \( y \)-axis is \( x = 0 \) (vertical line), and the \( x \)-axis is \( y = 0 \) (horizontal line). Wait, the options: "A vertical line that goes through \( k \) (\( k
eq0 \))" – no, origin is \( (0,0) \), so vertical line through origin is \( x = 0 \), which is the \( y \)-axis? Wait, no, wait: Wait, the question is "Which line of reflection is the vertical line that passes through the origin?". The \( y \)-axis is the vertical line \( x = 0 \) (passes through origin). Let's check options:

• "A horizontal line that goes through \( k \) (\( k \) is not zero)" – horizontal, so no.
• "A vertical line that goes through \( k \) (\( k

eq0 \))" – \( k
eq0 \), so not origin.

• "The \( y \)-axis" – \( y \)-axis is \( x = 0 \), vertical line through origin.
• "The \( x \)-axis" – horizontal, so no.

So the correct option is "The \( y \)-axis".

Answer:

right or left

Second Question (About Vertical Line of Reflection through Origin):