Question

26

Answer 1

Corrected Question

Ping lives at the corner of 3rd Street and 6th Avenue. Ari lives at the corner of 21st Street and 18th Avenue. There is a gym 2/3 the distance from Ping's home to Ari's home.  Where is the gym?

• 9th Street and 10th Avenue
• 12th Street and 12th Avenue
• 14th Street and 12th Avenue

• 15th Street and 14th Avenue

Answer:

(D)15th Street and 14th Avenue

Step-by-step explanation:

Ping's Location: (3rd Street, 6th Avenue)

Ari's Location: (21st Street, 18th Avenue)

The gym is at point P which is $\dfrac{2}{3}$ the distance from Ping's home to Ari's home.

That is, Point P divides the line segment in the ratio 2:1.

We use the section formula:

$(x,y)=\left(\dfrac{mx_2+nx_1}{m+n}, \dfrac{my_2+ny_1}{m+n}\right)$

m:n=2:1, $(x_1,y_1)=(3,6), (x_2,y_2)=(21,18)$

$=\left(\dfrac{2*21+1*2}{2+1}, \dfrac{2*18+1*6}{2+1}\right)\\=\left(\dfrac{45}{3}, \dfrac{42}{3}\right)\\=(15,14)$

The gym is located at 15th Street and 14th Avenue.