Reflection is the mirror image formed when the point is flipped over the line of reflection.

Plot the point K(- 3, 6).

So, the coordinates of the image are K′(3, 6).

A reflection flips a figure over a line of reflection. The reflected figure, or image, is the same as the original figure.

From the figure, it is clear that the figure is flipped over a line of reflection (the vertical line) and the reflected figure is the same as the original figure.

So, the transformation illustrated in the figure is reflection.

From the figure, PQ¯ is the reflection image of AB¯. So, y + 2 = 6 ⇒ y = 4.

From the figure, RQ¯ is the reflection image of CB¯. So, 2x - 2 = 8 ⇒ x = 5.

ΔABC is an equilateral triangle in which D is the mid point of BC¯. From the figure, AD¯ is median through A to BC¯.

Since medians are the perpendicular bisectors of the sides in an equilateral triangle, line l is the perpendicular bisector of BC¯.

So, the reflection of ΔABD in line l is ΔADC

ΔABD and ΔADC are congruent

So, area of ΔABD = area of ΔADC = 2.3 cm²

Given point is (x, y) and the line of reflection is y-axis, y-axis is the perpendicular bisector of the line segment joining (x, y) and (-x, y) .

So, the reflection image of P(x, y) in the y-axis is (-x, y) .

Since the triangle is reflected on the x-axis, the x-coordinate will not change.

Since A is 2 units up from the x-axis, the reflected point will be 2 units down from the x-axis.

The coordinates of point A′ are (-2 , -2)

Since the triangle is reflected on the x-axis, the x-coordinate will not change.

Since A is 4 units up from the x-axis, the reflected point will be 4 units down from the x-axis.

The coordinates of point A′ are (-2, -4).

When a point is reflected over a horizontal line, the x-coordinate remains the same and the sign of the y-coordinate changes.

The coordinates of the point after the reflection on x-axis is (4, 3).

When a point is reflected over a vertical line, the y-coordinate remains the same and the sign of the x-coordinate changes.

The coordinate of the point when reflected over the y-axis is (- 4, 3) as shown in the following figure.

The coordinates of the final image of point C' are (- 4, 3).

When a point is reflected over a vertical line the y-coordinate remains the same.

The point P(-2, -4) is reflected over the line x = 3.

The distance of the point from the line x = 3 is 2 + 3 = 5.

So, the image of the point will be 5 units away from the line x = 3.

The x-coordinate of the image of the point with respect to the coordinate axes = 5 + 3 = 8.

So, the coordinates of the image of the point P(-2, -4) along x = 3 are (8, -4).

To find the image of any point P(a, b) in the x-axis, keep the x-coordinate same and change the sign of the y-coordinate.

So, the image of the point P(- 5, - 8) in x-axis is (- 5, 8)