Answer
a. The coffee shop is located at the corner of $15$th St. and $12$th Ave
Coordinates: $(15, 12)$
b. $13$ blocks
Work Step by Step
We must first identify the coordinates based on the given.
The coordinates are:
Friend $1$: $(3, 7)$
Friend $2$: $(27, 17)$
a. We need to apply the midpoint formula using the given coordinates above:
$mp = \left( \dfrac{x_{1}+x_{2}}{2} , \dfrac{x_{1}+x_{2}}{2} \right)$
$mp = \left( \dfrac{3+27}{2} ,
\dfrac{7+17}{2} \right)$
$mp = (15, 12)$
Coffee Shop: $(15, 12)$
The Coffee Shop is located at the corner of $15$th St. and $12$th Ave.
b. We need to apply the distance formula using the coordinates of Friend $1$ and the Coffee Shop
Friend 1: $(3, 7)$
Coffee Shop: $(15, 12)$
$d = \sqrt { (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} }$
$d = \sqrt { (15 - 3)^{2} + (12 - 7)^{2} }$
$d = \sqrt { (144) + (25) }$
$d = \sqrt { (144) + (25) }$
$d = 13$
Both of them must walk $13$ blocks just to reach the coffee shop.
