Solved on Dec 06, 2023

Find the image of the point (2,3) under reflection across the line x=0.

STEP 1

Assumptions
1. The line of reflection is at $x=0$ .
2. The point to be reflected is $(2,3)$ .
3. The image of the point after reflection will be equidistant from the line of reflection but on the opposite side.

STEP 2

Understand the concept of reflection across a vertical line. When a point is reflected across a vertical line like $x=0$ , the $x$ -coordinate of the point changes sign, while the $y$ -coordinate remains the same.

STEP 3

Apply the reflection rules to the given point $(2,3)$ . Change the sign of the $x$ -coordinate to find the image of the point.
$x' = -x$

STEP 4

Calculate the new $x$ -coordinate for the image of the point.
$x' = -2$

STEP 5

Since the $y$ -coordinate remains the same after reflection across the line $x=0$ , we have:
$y' = y$

STEP 6

Calculate the $y$ -coordinate for the image of the point, which remains unchanged.
$y' = 3$

STEP 7

Combine the new $x$ and $y$ coordinates to get the image of the point $(2,3)$ after reflection across the line $x=0$ .
$Image\, point = (x', y')$

STEP 8

Substitute the calculated $x'$ and $y'$ into the image point.
$Image\, point = (-2, 3)$
The image of the point $(2,3)$ after reflection across the line $x=0$ is $(-2,3)$ .

Was this helpful?

Find the image of the point (2,3) under reflection across the line x=0.

STEP 1

Assumptions
1. The line of reflection is at $x=0$ .
2. The point to be reflected is $(2,3)$ .
3. The image of the point after reflection will be equidistant from the line of reflection but on the opposite side.

STEP 2

Understand the concept of reflection across a vertical line. When a point is reflected across a vertical line like $x=0$ , the $x$ -coordinate of the point changes sign, while the $y$ -coordinate remains the same.

STEP 3

Apply the reflection rules to the given point $(2,3)$ . Change the sign of the $x$ -coordinate to find the image of the point.
$x' = -x$

STEP 4

Calculate the new $x$ -coordinate for the image of the point.
$x' = -2$

STEP 5

Since the $y$ -coordinate remains the same after reflection across the line $x=0$ , we have:
$y' = y$

STEP 6

Calculate the $y$ -coordinate for the image of the point, which remains unchanged.
$y' = 3$

STEP 7

Combine the new $x$ and $y$ coordinates to get the image of the point $(2,3)$ after reflection across the line $x=0$ .
$Image\, point = (x', y')$

STEP 8

Substitute the calculated $x'$ and $y'$ into the image point.
$Image\, point = (-2, 3)$
The image of the point $(2,3)$ after reflection across the line $x=0$ is $(-2,3)$ .

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the image of the point (2,3) under reflection across the line x=0.

STEP 1

Assumptions1. The line of reflection is at x=0x=0x=0.2. The point to be reflected is (2,3)(2,3)(2,3).3. The image of the point after reflection will be equidistant from the line of reflection but on the opposite side.

STEP 2

Understand the concept of reflection across a vertical line. When a point is reflected across a vertical line like x=0x=0x=0, the xxx-coordinate of the point changes sign, while the yyy-coordinate remains the same.

STEP 3

Apply the reflection rules to the given point (2,3)(2,3)(2,3). Change the sign of the xxx-coordinate to find the image of the point.x′=−xx' = -xx′=−x

STEP 4

Calculate the new xxx-coordinate for the image of the point.x′=−2x' = -2x′=−2

STEP 5

Since the yyy-coordinate remains the same after reflection across the line x=0x=0x=0, we have:y′=yy' = yy′=y

STEP 6

Calculate the yyy-coordinate for the image of the point, which remains unchanged.y′=3y' = 3y′=3

STEP 7

Combine the new xxx and yyy coordinates to get the image of the point (2,3)(2,3)(2,3) after reflection across the line x=0x=0x=0.Image point=(x′,y′)Image\, point = (x', y')Imagepoint=(x′,y′)

STEP 8

Substitute the calculated x′x'x′ and y′y'y′ into the image point.Image point=(−2,3)Image\, point = (-2, 3)Imagepoint=(−2,3)The image of the point (2,3)(2,3)(2,3) after reflection across the line x=0x=0x=0 is (−2,3)(-2,3)(−2,3).

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Assumptions
1. The line of reflection is at $x=0$ .
2. The point to be reflected is $(2,3)$ .
3. The image of the point after reflection will be equidistant from the line of reflection but on the opposite side.

Understand the concept of reflection across a vertical line. When a point is reflected across a vertical line like $x=0$ , the $x$ -coordinate of the point changes sign, while the $y$ -coordinate remains the same.

Apply the reflection rules to the given point $(2,3)$ . Change the sign of the $x$ -coordinate to find the image of the point.
$x' = -x$

Calculate the new $x$ -coordinate for the image of the point.
$x' = -2$

Since the $y$ -coordinate remains the same after reflection across the line $x=0$ , we have:
$y' = y$

Calculate the $y$ -coordinate for the image of the point, which remains unchanged.
$y' = 3$

Combine the new $x$ and $y$ coordinates to get the image of the point $(2,3)$ after reflection across the line $x=0$ .
$Image\, point = (x', y')$

Substitute the calculated $x'$ and $y'$ into the image point.
$Image\, point = (-2, 3)$
The image of the point $(2,3)$ after reflection across the line $x=0$ is $(-2,3)$ .