Question

The reflection of (-2,3) with respect to y-axis is​

Answer 1

$\textsf{\large{\underline{Answer}:}}$

→ The reflection of (-2, 3) with respect to y-axis is (2, 3)

When we are reflecting a point in y-axis, the sign of abscissa or the x-coordinate value changes and the y-coordinate remains same.

So, -2 changes to 2 and 3 remains 3. Therefore, the point is (2, 3)

$\textsf{\large{\underline{To Be Noted}:}}$

1. When a point is reflected in x-axis, the value of ordinate (or y-coordinate) is negated.

Example: Suppose the point is (x, y). When reflected in x axis, the coordinate of the image will be (x, -y)

2. When a point is reflected in y-axis, the value of abscissa (or x-coordinate) is negated.

Example: Suppose the point is (x, y). When reflected in y axis, the coordinate of the image will be (-x, y)

3. When a point is reflected in origin, both the value of abscissa and ordinate is negated.

Example: Suppose the point is (x, y). When reflected in origin, the coordinate of the image will be (-x, -y)

4. Invariant Point: A point is said to be an invariant point with respect to a line if and only if the point lies on the line.

This means the coordinate of the point and it's image will be same.

Example: Suppose the coordinate of the point is (0, 0). When we are reflecting the point w.r.t origin, the coordinate of the point is (0, 0) which is same as the original one. So, it is an invariant point w.r.t origin.