Step: 1

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

Step: 2

Plot the point K(- 3, 6).

Step: 3

Step: 4

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

Correct Answer is : (3, 6)

Step: 1

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

Step: 2

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.

Step: 3

So, the transformation illustrated in the figure is reflection.

Correct Answer is : reflection

Step: 1

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

[Solve for y .]

Step: 2

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

[Solve for x .]

Correct Answer is : x = 5, y = 4

Step: 1

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

Step: 2

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

Step: 3

So, the reflection of ΔABD in line l is ΔADC

[Steps 1, 2.]

Step: 4

ΔABD and ΔADC are congruent

[Reflection is an isometry.]

Step: 5

So, area of ΔABD = area of ΔADC = 2.3 cm^{2}

[Reflection does not change area.]

Correct Answer is : 2.3 cm^{2}

Step: 1

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 ) .

Step: 2

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

Correct Answer is : (-x , y )

Step: 1

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

Step: 2

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

Step: 3

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

Correct Answer is : (- 2, - 2)

Step: 1

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

Step: 2

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

Step: 3

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

Correct Answer is : (- 2, - 4)

Step: 1

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

Step: 2

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

Step: 3

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

Step: 4

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

Step: 5

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

Correct Answer is : (- 4, 3)

Step: 1

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

Step: 2

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

Step: 3

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

Step: 4

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

Step: 5

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

Step: 6

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

Correct Answer is : (8, -4)

Step: 1

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.

Step: 2

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

Correct Answer is : (- 5, 8)

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- Reflection