Question

George decides to walk from his home to Tina's house down the street. On the way,

Answer 1

Answer:

The coordinates of the gas station are (5, 9)

Step-by-step explanation:

As given,

George begins at (2,3), ends at (9,17), and  stops at the gas station at (x,y). If the part to part ratio is 3:4

 A                   P                     B

(2, 3)             (x, y)                (9, 17)

           3         :             4

we use the Interval Division formula :

If P(x,y) lies on the interval A(x1,y1), B(x2,y2) such that AP:PB=a:b, with a and b positive, then

x= $\frac{bx1 + ax2}{a + b}$

y=$\frac{by1 + ay2}{a + b}$

Here , (x1, y1) = (2, 3)

          (x2, y2) = (9, 17)

           a : b = 3 : 4

⇒ x= $\frac{bx1 + ax2}{a + b}$ = $\frac{4(2) + 3(9)}{3 + 4} = \frac{8 + 27}{7} = \frac{35}{7} = 5$

   y=$\frac{by1 + ay2}{a + b}$ = $\frac{4(3) + 3(17)}{3 + 4} = \frac{12 + 51}{7} = \frac{63}{7} = 9$

∴ The coordinates of the gas station are (5, 9)