Math / Geometry

QuestionIf this triangle is reflected over the line $y=k$ , what are the coordinates for $y$ ? $(-2,-6)$ $(-6.2)$ 125 (6.2)

Studdy Solution

STEP 1

What is this asking? If we flip this triangle over the line $y = x$ , where does point J end up? Watch out! Don't mix up the x and y coordinates!
Reflecting over $y = x$ swaps the coordinates.
Reflecting over the x-axis changes the sign of the y-coordinate, and reflecting over the y-axis changes the sign of the x-coordinate.

STEP 2

1. Understand Reflection over $y = x$
2. Find the Reflected Point

STEP 3

Alright, so we're reflecting over the line $y = x$ .
What does that even mean?
Imagine folding your paper along the line $y = x$ .
Where would the triangle land?

STEP 4

Reflecting a point over $y = x$ swaps its x and y coordinates.
Think of it like this: the line $y = x$ acts like a mirror.
If a point is above the line, its reflection will be below, and vice-versa.
If a point is to the left of the line, its reflection will be to the right, and vice-versa.

STEP 5

Our point J has coordinates $(6, 2)$ .
The x-coordinate is 6, and the y-coordinate is 2.

STEP 6

To reflect J over the line $y = x$ , we simply swap the x and y coordinates!
So, the new x-coordinate will be the old y-coordinate, and the new y-coordinate will be the old x-coordinate.

STEP 7

Therefore, the reflected point J' will have coordinates $(2, 6)$ .
We swapped the 6 and the 2!

STEP 8

The coordinates of point J after reflecting over the line $y = x$ are $(2, 6)$ .

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QuestionIf this triangle is reflected over the line $y=k$ , what are the coordinates for $y$ ? $(-2,-6)$ $(-6.2)$ 125 (6.2)

Studdy Solution

STEP 1

STEP 2

1. Understand Reflection over $y = x$
2. Find the Reflected Point

STEP 3

Alright, so we're reflecting over the line $y = x$ .
What does that even mean?
Imagine folding your paper along the line $y = x$ .
Where would the triangle land?

STEP 4

Reflecting a point over $y = x$ swaps its x and y coordinates.
Think of it like this: the line $y = x$ acts like a mirror.
If a point is above the line, its reflection will be below, and vice-versa.
If a point is to the left of the line, its reflection will be to the right, and vice-versa.

STEP 5

Our point J has coordinates $(6, 2)$ .
The x-coordinate is 6, and the y-coordinate is 2.

STEP 6

To reflect J over the line $y = x$ , we simply swap the x and y coordinates!
So, the new x-coordinate will be the old y-coordinate, and the new y-coordinate will be the old x-coordinate.

STEP 7

Therefore, the reflected point J' will have coordinates $(2, 6)$ .
We swapped the 6 and the 2!

STEP 8

The coordinates of point J after reflecting over the line $y = x$ are $(2, 6)$ .

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QuestionIf this triangle is reflected over the line y=ky=ky=k, what are the coordinates for yyy ? (−2,−6)(-2,-6)(−2,−6) (−6.2)(-6.2)(−6.2) 125 (6.2)

Studdy Solution

STEP 1

STEP 2

1. Understand Reflection over y=xy = xy=x2. Find the Reflected Point

STEP 3

Alright, so we're reflecting over the line y=xy = xy=x.What does *that* even mean?Imagine folding your paper along the line y=xy = xy=x.Where would the triangle land?

STEP 4

Reflecting a point over y=xy = xy=x swaps its x and y coordinates.Think of it like this: the line y=xy = xy=x acts like a mirror.If a point is above the line, its reflection will be below, and vice-versa.If a point is to the left of the line, its reflection will be to the right, and vice-versa.

STEP 5

Our point J has coordinates (6,2)(6, 2)(6,2).The x-coordinate is **6**, and the y-coordinate is **2**.

STEP 6

To reflect J over the line y=xy = xy=x, we simply swap the x and y coordinates!So, the new x-coordinate will be the old y-coordinate, and the new y-coordinate will be the old x-coordinate.

STEP 7

Therefore, the reflected point J' will have coordinates (2,6)(2, 6)(2,6).We swapped the **6** and the **2**!

STEP 8

The coordinates of point J after reflecting over the line y=xy = xy=x are (2,6)(2, 6)(2,6).

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QuestionIf this triangle is reflected over the line $y=k$ , what are the coordinates for $y$ ? $(-2,-6)$ $(-6.2)$ 125 (6.2)

1. Understand Reflection over $y = x$
2. Find the Reflected Point

Alright, so we're reflecting over the line $y = x$ .
What does that even mean?
Imagine folding your paper along the line $y = x$ .
Where would the triangle land?

Reflecting a point over $y = x$ swaps its x and y coordinates.
Think of it like this: the line $y = x$ acts like a mirror.
If a point is above the line, its reflection will be below, and vice-versa.
If a point is to the left of the line, its reflection will be to the right, and vice-versa.

Our point J has coordinates $(6, 2)$ .
The x-coordinate is 6, and the y-coordinate is 2.

To reflect J over the line $y = x$ , we simply swap the x and y coordinates!
So, the new x-coordinate will be the old y-coordinate, and the new y-coordinate will be the old x-coordinate.

Therefore, the reflected point J' will have coordinates $(2, 6)$ .
We swapped the 6 and the 2!

The coordinates of point J after reflecting over the line $y = x$ are $(2, 6)$ .