Question

The point (a,b) is reflected across the line y=x and then across the x-axis. Which of the following are the coordinates of its final image point in terms of a and b?(1) (-b,-a)(2) (-b,a)(3) (b,-a)(4) (-a,-b)

Answer 1

When a point is reflected across the line, y = x, the x and y coordinates changes places. Given that the coordinates of the original point is (a, b), the coordinate of the new point would be (b, a)

Again, this new point was reflected across the x axis. Recall, if reflection is done across the x axis, the sign of the x coordinate remains the same while the sign of the y coordinate is reversed,

Therefore, the coordinates of its final image point in terms of a and b is (b, - a)

The correct option is number 3