Math Snap

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!

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