Which graph shows a triangle and its reflection image over t

Which graph shows a triangle and its reflection image over the x-axis?

A.

B.

C.

D.

Solution

In order to respond to this question ,let us observe all the four options.

For an isometry to make a reflection of itself over any axis, it is a necessary condition that each point and its corresponding reflection with respect to the axis of reflection should be equidistant from the axis of reflection /symmetry.

1. In this we observe that both the images are similar to each other and are reflection of each other with respect to y axis .Thus this option is discarded.

2. If we compare corresponding points of the two triangles we will observe that they are not equidistant from any axis .Hence this option is also discarded .

3. If we compare corresponding points of the two triangles we will observe that they are not equidistant from any axis .Hence this option is also discarded .

4. Comparing the two triangles we can see that all corresponding point of both triangles are equidistant with respect to x axis and hence this is the right option .It shows a triangle and its reflection over the x axis .