Question

On a coordinate plane, a graph shows Street on the x-axis and Avenue on the y-axis. A line is drawn from Tia to Lei. Tia is at (4, 8) and Lei is at (12, 20).

Tia lives at the corner of 4th Street and 8th Avenue. Lei lives at the corner of 12th Street and 20th Avenue. The fruit market is Three-fourths the distance from Tia’s home to Lei's home.

x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1

y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1

Where is the fruit market?

6th Street and 11th Avenue
10th Street and 17th Avenue
9th Street and 15th Avenue
8th Street and 14th Avenue

Answer 1

B

Explanation:

10th Street and 17th Avenue

Answer 2

B. At the corner of 10th Street and 17th Avenue.

Explanation:

The point (x,y) which divides the segment AB with endpoints at
`A(x_1,y_1)` and
`B(x_2,y_2)` in ratio
`m:n` has coordinates

`x=(nx_1+nx_2)/(m+n)\\ \\y=(ny_1+ny_2)/(m+n)`

In your case,

`T(4,8)`

`L(12,20)`

The fruit market (F) is three-fourths the distance from Tia’s home to Lei's home, then
`TM:TL=3:4` or
`TM:ML=3:1`

Thus,

`x=(1\cdot 4+3\cdot 12)/(3+1)=(4+36)/(4)=(40)/(4)=10\\ \\y=(1\cdot 8+3\cdot 20)/(3+1)=(8+60)/(4)=(68)/(4)=17`

So, the fruit market is at point
`F(10,17)` which ,=means it is placed at the corner of 10th Street and 17th Avenue.