To determine the distance from your house at point [tex]\( C \)[/tex] to your school at point [tex]\( E \)[/tex], we need to add the distances between the given points along the route.
You are provided with the following distances:
- The distance from your house at point [tex]\( C \)[/tex] to the post office at point [tex]\( D \)[/tex] is [tex]\( CD = 1.7 \)[/tex] miles.
- The distance from the post office at point [tex]\( D \)[/tex] to the school at point [tex]\( E \)[/tex] is [tex]\( DE = 2.4 \)[/tex] miles.
Since point [tex]\( D \)[/tex] is directly on the path from point [tex]\( C \)[/tex] to point [tex]\( E \)[/tex], we can find the total distance from point [tex]\( C \)[/tex] to point [tex]\( E \)[/tex] by adding the two given distances. This means that the total distance [tex]\( CE \)[/tex] is calculated as follows:
[tex]\[
CE = CD + DE
\][/tex]
Given:
[tex]\[
CD = 1.7 \text{ miles}
\][/tex]
and
[tex]\[
DE = 2.4 \text{ miles}
\][/tex]
Adding these distances gives:
[tex]\[
CE = 1.7 \text{ miles} + 2.4 \text{ miles} = 4.1 \text{ miles}
\][/tex]
Therefore, the distance from your house to your school is [tex]\( 4.1 \)[/tex] miles.
So, the correct answer is:
[tex]\[
\boxed{4.1 \text{ miles}}
\][/tex]
This corresponds to option B in the given choices.
