Question

26

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 į the distance from Ping's home to Ari's home.
24
22
20
n
Ari (21.18)
7
x =
18
(x2 – x) + x3
mi+n
16
Avenue
14
-- ( , Jive - y) +
12
10
Where is the gym?
00
6
Ping (36)
4
2
9th Street and 10th Avenue
12th Street and 12th Avenue
0 14th Street and 12th Avenue
15th Street and 14th Avenue
2
x
4 6 8 10 12 14 16 18 20 22 24 26
Street

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

Explanation:

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

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

The gym is at point P which is
`(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((mx_2+nx_1)/(m+n), (my_2+ny_1)/(m+n)\right)`

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

`=\left((2*21+1*2)/(2+1), (2*18+1*6)/(2+1)\right)\\=\left((45)/(3), (42)/(3)\right)\\=(15,14)`

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