Question

On a coordinate plane, triangle P Q R has points (3, 0), (1, negative 2), (4, negative 2).Triangle PQR is reflected over the line y = x.

What is the coordinate of the image point R’?

Answer 1

P'(0, 3)

- Q'(-2, 1)

- R'(-2, 4)

Explanation:

When triangle PQR is reflected over the line y = x, each point of the original triangle is transformed to a new point with its x and y coordinates swapped. This is because reflecting over the line y = x effectively mirrors the points across the line.

Let's find the reflected points of triangle PQR:

Original points:

- P(3, 0)

- Q(1, -2)

- R(4, -2)

Reflecting over the line y = x:

- The (x) coordinate of each point becomes its new \(y\) coordinate.

- The (y) coordinate of each point becomes its new \(x\) coordinate.

Reflected points:

- For P(3, 0), the reflection becomes P'(0, 3).

- For Q(1, -2), the reflection becomes Q'(-2, 1).

- For R(4, -2), the reflection becomes R'(-2, 4).

So, the reflected triangle P'Q'R' has points:

- P'(0, 3)

- Q'(-2, 1)

- R'(-2, 4)