Help please worth 57 points

Step-by-step explanation:

A line segment is always similar to another line segment, because we can always map one into the other using only dilation a and rigid transformations

we know that

A dilation is  a Non-Rigid Transformations that change the structure of our original object. For example, it can make our object bigger or smaller using scaling.

The dilation produce similar figures

In this case, it would be lengthening or shortening a line. We can dilate any line to get it to any desired length we want.

A rigid transformation, is a transformation that preserves distance and angles, it does not change the size or shape of the figure. Reflections, translations, rotations, and combinations of these three transformations are rigid transformations.

so

If we have two line segments XY and WZ,  then it is possible to use dilation and rigid transformations to map line segment XY to line segment WZ.

The first segment XY would map to the second segment WZ

therefore

A line segment is always similar to another line segment, because we can always map one into the other using only dilation a and rigid transformations

Always, always.

Hint: To find the mean marks from the given data, we have to convert it into frequency distribution. We can write below 10 as 0-10, below 20 as 10-20 and so on. The corresponding frequencies ( fi) can be found by subtracting the previous number of students from the current number of students.