Answer
$(a)$ $5$ $blocks$
$(b)$ Walking distance: $31$ $blocks$
Straight-line distance: $25$ $blocks$
$(c)$ These two points $P$ and $Q$ are aligned in a straight line, either vertically (on the same street) or horizontally (on the same avenue).
Work Step by Step
$(a)$ The straight line distance can simply be found using Pythagorean Theorem.
$d=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5$ $blocks$
$(b)$ Let's imagine the map as a coordinate plane (See the image below). Let the corner of $4^{th}$ street and $2^{nd}$ avenue be point $A(4, 2)$. So the $11^{th}$ street and $26^{th}$ avenue will be point $B(11, 26)$
As it is clear from the image below, the walking distance is: $(11-4)+(26-2) = 7+24 = 31$ $blocks$
$7$ blocks to the East and $24$ blocks to the North.
To calculate the straight-line distance, we will use the Pythagorean Theorem again.
$d=\sqrt{7^2+24^2}=\sqrt{49+576}=\sqrt{625}=25$ $blocks$
$(c)$ If a walking distance and a straight line distance between any $2$ points are equal to each other then these two points are aligned in a straight line, either vertically (on the same street) or horizontally (on the same avenue).
