Question

The diagram is drawn on a square grid. Of the triangles marked P, Q, R, and S, which is the image of triangle X under a reflection in the line MN?

A) P
B) Q
C) R
D) S

Answer 1

Hint:
The line of symmetry is the line that divides the image into two mirror images. It can be vertical, horizontal, or diagonal. It is also called reflection symmetry. So fold the diagram along the line MN and see which image of the triangle coincides with the triangle X.

Complete step by step solution:
We are given a diagram drawn on a square grid in which there are five rectangles present. We have to find the image of triangle X under a reflection in the line MN.

We know that the line of symmetry is an imaginary line or axis along which the figure when folded gives symmetrical or identical halves. These halves are mirror images of each other.
So we will fold the square grid along the line MN and see that the triangle X overlaps Q on folding.

If it is difficult to fold the whole square grid fold only the area selected in Red square in the above diagram. When we fold it we see it is seen like this-

So we can clearly see that the reflection image of triangle X is the image of triangle Q.

Answer-The correct answer is option B.

Note:
In line of symmetry, the following points are important-
The folded sides of the figure must coincide if it is folded along the line of symmetry.
It is not necessary that all lines that divide a figure into two congruent halves or mirror images are lines of symmetry. For example- The diagonal of a rectangle divides it into two congruent triangles but when we fold the figure along the diagonal the lines of one side do not coincide with the other side. Hence the diagonal of a triangle is not a line of symmetry.
The lines of symmetry of regular polygons are equal to the number of sides.