Question

Point N has coordinates (−1, 2). Point M is symmetric to point N with respect to the line y = x.

What are the coordinates of point M?


(2, −2)


(1, −2)


(−2, 1)


(2, −1)

Answer 1

Explanation:

To find the coordinates of point M, we need to reflect point N across the line y = x. This line corresponds to the diagonal of the coordinate plane, where the x and y coordinates are equal.

To reflect a point across a line, we can use the following formula:

(x', y') = (2a - x, 2b - y)

where (a, b) are the coordinates of the point being reflected, and (x', y') are the coordinates of the reflected point.

In this case, (a, b) = (-1, 2) and the line of reflection is y = x. So we have:

x = -1, y = 2

a = -1, b = 2

x' = y = 2

y' = x = -1

Using the formula above, we can find the coordinates of point M:

(x', y') = (2a - x, 2b - y) = (2(-1) - (-1), 2(2) - 2) = (-2 + 1, 4 - 2) = (-1, 2)

Therefore, the coordinates of point M are (-1, 2), which is the same as the coordinates of point N. So point M is simply a reflection of point N across the line y = x.