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Solved problems for the chapter:

Transformation of 2-D points and shapes

View the theory »

Cartesian coordinate system

1. Point in rectangular coordinate system

2. Quadrants

3. Mirroring

3.1. Mirroring across the abscissa axis

3.2. Mirroring across the ordinate axis

3.3. Mirroring over the starting point

4. Sets of points in the plane

5. Forum

↓ Show theory [1] ↓

Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:transformation_of_2-d_points_and_shapes/5176/

Example 1.

You can make patterns on square grids using 5 square tiles.

This pattern below has one line of symmetry.

Use 5 square tiles to draw a pattern on the grid below that has more than one line of symmetry.

the problem is without solution steps

Example 2.

The pattern below is not finished. Draw one more triangle so that the pattern looks the same when it is rotated through one or more right angles.

the problem is without solution steps

A is the reflection of the point T over the line p. The point B is the reflection of the point T over the line q. The distance between points and is . The distance between point and line is :

Calculate the distance of the point T from the line q.

There are some blue dots representing pre-images in the figure and a few red dots that are their images across the line p.

Fill in the picture with the missing dots.

Lines AB, CD and EF are given. Reflect them over the line p. Also write down the rules of mappings.

Reflect over the line p.

Color the minimum number of empty circles so that the image is reflected with respect to the bisector s.

Remove the minimum number of circles so that the image is symmetric with respect to the bisector s.

In the set of points, find the pair (the pre-image and the image) reflecting over the line p.

10.

There are some blue pre-image points and red image points in the picture. Are these pre-image points reflected over a point or over a straight line?

11.

Rotating around the point S and moving parallel in the direction of the line SB (exactly in that order) move the point A to the position of the point B. Choose a shorter route.

12.

Plot the given points in the coordinate system, then mirror them across the abscissa axis and write down the new coordinates of the points.

A(3, 4), B(-1, 3), C(0, 2) and D(-3,-2)

13.

Plot the given points in the coordinate system, then mirror them across the ordinate axis and write down the new coordinates of the points.

A(3, 4), B(-1, 3), C(-2, 0) and D(-1, -3)

14.

Three of the points in the sketch below represent: the pre-image, the image and the point through which the original is reflected. Mark them and write down the rules of reflection.

15.

Rotate over point T. Also write down all rotation rules.

16.

Points A and B are reflected according to the rule:

Connect the points A, B, A' and B' and name the shape ABA'B'.

17.

Below are three points. Reflect all points and write down the reflecting rules.

18.

Given line AB, 4 cm long. Reflect an end over the other and mark the image with A' or B'. What is the length of the line B'A'? How many times the value of the original line AB is this?

Also write down the rules of reflection.

19.

Reflect AB, TC and DE over point T and write down the rules of reflection.