Q20. - Algebra 2

Question

20. REAL ESTATE In John’s town, the numbered streets and avenues form a grid. He belongs to a gym at the corner of 12th Street and 15th Avenue, and the deli where he works is at the corner of 4th Street and 5th Avenue. He wants to rent an apartment halfway between the two. In what area should he look?

Step-by-Step Solution

Answer

The area is at the corner of 8th Street and 10th Avenue.

Step 1.Given

In John’s town, the numbered streets and avenues form a grid. He belongs to a gym at the corner of 12th Street and 15th Avenue, and the deli where he works is at the corner of 4th Street and 5th Avenue.

Step 2.To determine

He wants to rent an apartment halfway between the two. In what area should he look?

Step 3.Calculation

From the given part we can make two coordinates. 

The coordinate of the gym is (12, 15).

The coordinate of the deli is (4, 5).

If he wants to rent an apartment halfway between the two, he should take the midpoint of the two points. That is:

 

$\begin{array}{l}\left(\frac{12+4}{2},\frac{15+5}{2}\right)\\ =\left(\frac{16}{2},\frac{20}{2}\right)\\ =\left(8,10\right)\end{array}$

It means the area is at the corner of 8th Street and 10th Avenue.