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# Common Mistakes Made in ICSE Class 10 Board Exams Chapter Reflection

Reflection is the chapter from the unit Co-ordinate Geometry in the ICSE Class 10 syllabus. It is quite an easy chapter to attempt, still, mistakes are made by students in plotting graphs. To avoid major as well as minor mistakes in this chapter, let us try to understand the areas wherein mistakes are expected and try to overcome them.

Mistake in not using the SCALE provided in the question

Whenever the graph is to be plotted, the Scale of a graph is the most important thing. We can take the scale of the graph as per the points given for plotting. But, if the scale to be taken is already provided in the question, we are NOT supposed to change the scale at our convenience. We need to maintain the same scale given in question.

Question:

Use a graph paper for this question: (Take 2 cm = 1 unit on both axes).

Also, the scale provided in the question is often not read by students in a hurry, resulting in them settling on their scale.

It is a powerful suggestion to read the question properly and NOT MAKE MISTAKE in taking SCALE.

Mistakes in REFLECTING points on X-axis, Y-axis and Origin

Most often, it is asked to reflect the plotted points on the X-axis or Y-axis or at the Origin. And, we all know that there are certain rules for reflecting the points. Let us quickly check that!

Mx(x, y) ------ Reflected in X-axis ------ Sign of ordinate changes ------ Mx(x, –y)
My(x, y) ------ Reflected in Y-axis ------ Sign of abscissa changes ------ My(–x, y)
Mo(x, y) ------ Reflected in Origin ------ Signs of abscissa and ordinate both changes ------ Mo(–x, –y)

Let us check the solution for the below question:

Question:

Reflect point A(3, 5) in the X-axis, Y-axis and Origin and name the images as Aʹ, Aʹʹ and  Aʹʹʹ, respectively.

Reflection of point A(3, 5) in the X-axis

Reflection of point A(3, 5) in the Y-axis

Here, students plot point A(3, 5) correctly but make mistakes in reflecting the point. While reflecting a point in the X-axis, instead of changing the sign of ordinate, students change the sign of abscissa. And the same case happens while reflecting a point in the Y-axis. Hence, the plotted points are incorrect.

Reflecting a point in the origin is most of the time done correctly.

Quite strange, but some students plot the points correctly, even reflect the points correctly in both the axes and origin, but forget to label the points they plotted on the graph. This may also lead to a reduction in marks.

Mistake in NAMING the FIGURE formed in a graph

After reflecting the points in both the axes and origin, sometimes it is asked to join the points and name the figure formed.

Let us see the figure formed in the below graph.

The correct name of the figure is Octagon. But looking at the figure, students give a variety of names such as hexagon, pentagon, star and many more. All these names are incorrect.

PRACTICE QUESTIONS

Question 1: Points (4, 0) and (-3, 0) are invariant points under reflection in the line L1. Points (0, -2) and (0, 3) are invariant points on reflection in L2.

1. Name the lines L1 and L2
2. Write down the images of point P(1, 4) and q(-3, -5) on reflection in L1. Name the images as Pʹ and Qʹ respectively.
3. Write down the images of point P(1, 4) and q(-3, -5) on reflection in L2. Name the images as Pʹʹ and Qʹʹ respectively.
4. State or describe a single transformation that maps Pʹ to Pʹʹ.
Detailed solution can be viewed here.

Question 2: Plot ∆ABC whose vertices are A(3, 1), B(5, 0) and C(7, 4). On the same graph, draw the image ∆AʹBʹCʹ of ∆ABC under reflection in the line x = 2.